diff --git a/resources/boost/skills/livewire-material-development/SKILL.md b/resources/boost/skills/livewire-material-development/SKILL.md
index 02d87a4f..00c3bc2b 100644
--- a/resources/boost/skills/livewire-material-development/SKILL.md
+++ b/resources/boost/skills/livewire-material-development/SKILL.md
@@ -261,7 +261,18 @@ M3's plain tooltip, standalone around any trigger: `<x-tooltip text="Copy link"
 </x-menu>
 ```
 
-`<x-menu>`: `trigger` slot (its first button or link becomes the menu button, and the menu hangs on that button — a `position: fixed` trigger such as `<x-button fab>` carries it along, and a menu with no room flips to the other side, end or both), `label`, `position` (`bottom-start` default, `bottom-end`, `top-start`, `top-end`), `vibrant`. `<x-menu-item>`: `label`, `icon`, `icon-class` (classes for the leading icon; a colour there paints it, a selected item's too, but not a disabled one's — `icon-class="text-sport-run"`), `icon-right`, `description`, `shortcut`, `link`, `external`, `selected` (makes it a `menuitemcheckbox`, ticked at its end unless it has an `icon-right`), `current` (for a menu of places: marks the page you are on with `aria-current="page"` in secondary-container, never a checked choice), `badge` (`true` for a dot, or a count, at the end of the row), `disabled`, `keep-open`. Choosing an item closes the menu unless `keep-open`; a second press on the menu button closes it too. An open menu stays open while the Livewire component around it renders, a `keep-open` item's own `wire:click` included. Keyboard: arrows, Home, End, a letter, Escape (focus returns to the trigger), Tab; a `disabled` item keeps its place in that order, as M3 asks, but cannot be activated. A menu longer than the window scrolls.
+`<x-menu>`: `trigger` slot (its first button or link becomes the menu button, and the menu hangs on that button — a `position: fixed` trigger such as `<x-button fab>` carries it along, and a menu with no room flips to the other side, end or both), `label`, `position` (`bottom-start` default, `bottom-end`, `top-start`, `top-end`), `vibrant`. `<x-menu-item>`: `label`, `icon`, `icon-class` (classes for the leading icon; a colour there paints it, a selected item's too, but not a disabled one's — `icon-class="text-sport-run"`), `icon-right`, `description`, `shortcut`, `link`, `external`, `selected` (makes it a `menuitemcheckbox`, ticked at its end unless it has an `icon-right`), `current` (for a menu of places: marks the page you are on with `aria-current="page"` in secondary-container, never a checked choice), `badge` (`true` for a dot, or a count, at the end of the row), `disabled`, `keep-open`, `submenu`. Choosing an item closes the menu unless `keep-open`; a second press on the menu button closes it too. An open menu stays open while the Livewire component around it renders, a `keep-open` item's own `wire:click` included. Keyboard: arrows, Home, End, a letter, Escape (focus returns to the trigger), Tab; a `disabled` item keeps its place in that order, as M3 asks, but cannot be activated. A menu longer than the window scrolls.
+
+`submenu` makes an item a menu of its own — the slot holds the nested `<x-menu-item>`s instead of a label, and they open beside it, on its end, flipping to its start where the window has no room:
+
+```blade
+<x-menu-item label="Export as" icon="download" submenu>
+    <x-menu-item label="ZIP" icon="folder_zip" wire:click="exportZip" />
+    <x-menu-item label="PDF" icon="picture_as_pdf" wire:click="exportPdf" />
+</x-menu-item>
+```
+
+The item says so with `aria-haspopup="menu"`, `aria-expanded` and a chevron; Right, Enter or Space open it on its first item, Left or Escape close it and come back, and on a fine pointer resting on the item opens it. Choosing anything inside closes the whole menu. Arrows stay inside the list they are in. M3 calls submenus a large-screen pattern — on a phone give the menu `sheet-at-compact`, or keep the list flat.
 
 ### `<x-button-group>`
 
diff --git a/resources/css/components/menu.css b/resources/css/components/menu.css
index e03404d0..5226b775 100644
--- a/resources/css/components/menu.css
+++ b/resources/css/components/menu.css
@@ -1,7 +1,7 @@
 /*
- * The exposed dropdown menu — the list a field drops open.
+ * The menus: the exposed dropdown a field drops open, and what `<x-menu>` cannot say in utilities.
  *
- * Two lists wear it, so a form reads as one family:
+ * Two lists wear the dropdown, so a form reads as one family:
  *
  *   - `<x-select>`'s: the native <select>, opted into the browser's customizable select
  *     (`appearance: base-select`). `::picker(select)` is the menu and each <option> a row, while the
@@ -20,6 +20,29 @@
  * paints option colours into its native list would otherwise show a half-painted one.
  */
 
+/*
+ * `<x-menu>` and the submenus inside it.
+ *
+ * A submenu is a popover of its own nested in the menu's, so it cannot take the container colour
+ * from a class the item knows nothing about: the menu declares the pair as custom properties,
+ * which a nested popover inherits down the DOM whatever the top layer does with its painting. The
+ * fallbacks are the standard menu's, for a submenu in some other list (a FAB menu's).
+ */
+[data-menu] {
+    --material-menu-surface: var(--md-sys-color-surface-container-low);
+    --material-menu-ink: var(--md-sys-color-on-surface);
+}
+
+[data-menu][data-vibrant] {
+    --material-menu-surface: var(--md-sys-color-tertiary-container);
+    --material-menu-ink: var(--md-sys-color-on-tertiary-container);
+}
+
+[data-submenu] {
+    background: var(--material-menu-surface, var(--md-sys-color-surface-container-low));
+    color: var(--material-menu-ink, var(--md-sys-color-on-surface));
+}
+
 .field-menu {
     max-block-size: 18rem;
     overflow-y: auto;
diff --git a/resources/js/menu.js b/resources/js/menu.js
index 9462d03b..f51379be 100644
--- a/resources/js/menu.js
+++ b/resources/js/menu.js
@@ -1,5 +1,6 @@
 /**
  * `materialMenu`: the behaviour of `<x-menu>` — WAI-ARIA's menu button pattern on a popover.
+ * `materialSubmenu`: the same pattern one level in, for `<x-menu-item submenu>`.
  *
  * The menu button is the trigger's first button or link. Its ARIA attributes are written by
  * script, which a Livewire morph removes along with anything else the server did not render,
@@ -12,6 +13,13 @@
  * so the menu opened there. Script moves the name onto the menu button, beside any name the button
  * carries itself (a button's tooltip anchors on it too), and moves it again after every morph,
  * which puts the server's attributes, and a fresh name, back.
+ *
+ * A submenu's popover sits inside its parent's, so the browser keeps the two open together — a
+ * nested `popover="auto"` light-dismisses only down to its DOM ancestor — and closes the inner one
+ * when the outer goes. Its trigger *is* the item, which the server names itself, so the two pieces
+ * that exist only for a wrapper (moving the anchor name, and finding the button inside the trigger
+ * slot) are overridden away. `items()` stops at the popover it belongs to, so the arrow keys in a
+ * menu never walk into an open submenu's rows, nor a submenu's back out into its parent's.
  */
 const ITEMS = '[role="menuitem"], [role="menuitemcheckbox"], [role="menuitemradio"]'
 
@@ -21,244 +29,332 @@ const ITEMS = '[role="menuitem"], [role="menuitemcheckbox"], [role="menuitemradi
 // click.
 const REOPEN_GUARD_MS = 250
 
-document.addEventListener('alpine:init', () => {
-    window.Alpine.data('materialMenu', () => ({
-        closedAt: -Infinity,
-        anchored: null,
-        returnFocus: true,
-        focusWasInside: false,
-        listeners: [],
+// A submenu opens after the pointer has rested on its item for a moment, and closes a moment after
+// it leaves the pair — long enough to cross the gap between them. APG's menu pattern asks for both
+// delays. A coarse pointer has no hover to speak of, so there it opens on the press instead.
+const HOVER_OPEN_MS = 180
+const HOVER_CLOSE_MS = 320
 
-        init() {
-            const menu = this.$refs.menu
+const menu = () => ({
+    closedAt: -Infinity,
+    anchored: null,
+    returnFocus: true,
+    focusWasInside: false,
+    listeners: [],
 
-            this.label()
+    init() {
+        const menu = this.$refs.menu
+
+        this.label()
+        this.anchor()
+
+        // A morph rewrites the wrapper's style with this render's name and the button's without
+        // it, takes the button's ARIA attributes away and gives the popover a new id; the
+        // observer runs before the next frame is drawn, so an open menu never moves and its
+        // button never shows it shut.
+        const observer = new MutationObserver(() => {
             this.anchor()
+            this.label()
+        })
 
-            // A morph rewrites the wrapper's style with this render's name and the button's without
-            // it, takes the button's ARIA attributes away and gives the popover a new id; the
-            // observer runs before the next frame is drawn, so an open menu never moves and its
-            // button never shows it shut.
-            const observer = new MutationObserver(() => {
-                this.anchor()
-                this.label()
-            })
+        observer.observe(this.$refs.trigger, {
+            attributes: true,
+            attributeFilter: ['style', 'aria-haspopup', 'aria-controls', 'aria-expanded'],
+            childList: true,
+            subtree: true,
+        })
+        observer.observe(menu, { attributes: true, attributeFilter: ['id'] })
+        this.listeners.push(() => observer.disconnect())
 
-            observer.observe(this.$refs.trigger, {
-                attributes: true,
-                attributeFilter: ['style', 'aria-haspopup', 'aria-controls', 'aria-expanded'],
-                childList: true,
-                subtree: true,
-            })
-            observer.observe(menu, { attributes: true, attributeFilter: ['id'] })
-            this.listeners.push(() => observer.disconnect())
+        // Only closes the browser starts — Escape, a press outside — arrive here alone; open()
+        // and close() have already done their part, synchronously, because this event is
+        // queued and a screen reader or a test reading aria-expanded in between would be told
+        // the menu is shut.
+        // Whether focus was in the menu is read before it closes: once closed, a browser may
+        // already have handed focus to what had it before the menu opened (WebKit does, when
+        // that was a focusable region around the trigger).
+        this.listen(menu, 'beforetoggle', (event) => {
+            this.focusWasInside = event.newState === 'closed' && menu.contains(document.activeElement)
 
-            // Only closes the browser starts — Escape, a press outside — arrive here alone; open()
-            // and close() have already done their part, synchronously, because this event is
-            // queued and a screen reader or a test reading aria-expanded in between would be told
-            // the menu is shut.
-            // Whether focus was in the menu is read before it closes: once closed, a browser may
-            // already have handed focus to what had it before the menu opened (WebKit does, when
-            // that was a focusable region around the trigger).
-            this.listen(menu, 'beforetoggle', (event) => {
-                this.focusWasInside = event.newState === 'closed' && menu.contains(document.activeElement)
+            if (event.newState === 'closed') {
+                this.closedAt = performance.now()
+            }
+        })
 
-                if (event.newState === 'closed') {
-                    this.closedAt = performance.now()
-                }
-            })
+        this.listen(menu, 'toggle', (event) => {
+            const opened = event.newState === 'open'
 
-            this.listen(menu, 'toggle', (event) => {
-                const opened = event.newState === 'open'
+            this.control()?.setAttribute('aria-expanded', String(opened))
 
-                this.control()?.setAttribute('aria-expanded', String(opened))
-
-                if (opened) {
-                    return
-                }
-
-                if (this.returnFocus && (this.focusWasInside || menu.contains(document.activeElement))) {
-                    this.control()?.focus()
-                }
-
-                this.focusWasInside = false
-            })
-
-            // A press outside closes the menu without pulling focus back to the trigger.
-            this.listen(document, 'pointerdown', (event) => {
-                if (!menu.contains(event.target) && !this.$refs.trigger.contains(event.target)) {
-                    this.returnFocus = false
-                }
-            })
-        },
-
-        control() {
-            return this.$refs.trigger.querySelector('button, a[href], [tabindex]')
-        },
-
-        /**
-         * Moves the anchor name the server gave the wrapper onto the menu button. The wrapper holds a
-         * name only as rendered — this render's, which the popover's `position-anchor` matches — so
-         * it is read there.
-         */
-        anchor() {
-            const trigger = this.$refs.trigger
-            const control = this.control()
-            const rendered = trigger.style.getPropertyValue('anchor-name').trim()
-            const name = rendered.startsWith('--') ? rendered : this.anchored
-
-            // No menu button, or an engine without anchor positioning: the wrapper keeps the name.
-            if (!control || !name) {
+            if (opened) {
                 return
             }
 
-            const names = control.style
-                .getPropertyValue('anchor-name')
-                .split(',')
-                .map((each) => each.trim())
-                .filter((each) => each.startsWith('--'))
-
-            if (!names.includes(name)) {
-                control.style.setProperty('anchor-name', [...names.filter((each) => each !== this.anchored), name].join(', '))
+            if (this.returnFocus && (this.focusWasInside || menu.contains(document.activeElement))) {
+                this.control()?.focus()
             }
 
-            this.anchored = name
+            this.focusWasInside = false
+        })
 
-            if (rendered !== '') {
-                trigger.style.removeProperty('anchor-name')
+        // A press outside closes the menu without pulling focus back to the trigger.
+        this.listen(document, 'pointerdown', (event) => {
+            if (!menu.contains(event.target) && !this.$refs.trigger.contains(event.target)) {
+                this.returnFocus = false
             }
-        },
+        })
+    },
 
-        /** Writes only what differs: the observer that calls this watches these same attributes. */
-        label() {
-            const control = this.control()
+    control() {
+        return this.$refs.trigger.querySelector('button, a[href], [tabindex]')
+    },
 
-            if (!control) {
-                return
+    /**
+     * Moves the anchor name the server gave the wrapper onto the menu button. The wrapper holds a
+     * name only as rendered — this render's, which the popover's `position-anchor` matches — so
+     * it is read there.
+     */
+    anchor() {
+        const trigger = this.$refs.trigger
+        const control = this.control()
+        const rendered = trigger.style.getPropertyValue('anchor-name').trim()
+        const name = rendered.startsWith('--') ? rendered : this.anchored
+
+        // No menu button, or an engine without anchor positioning: the wrapper keeps the name.
+        if (!control || !name) {
+            return
+        }
+
+        const names = control.style
+            .getPropertyValue('anchor-name')
+            .split(',')
+            .map((each) => each.trim())
+            .filter((each) => each.startsWith('--'))
+
+        if (!names.includes(name)) {
+            control.style.setProperty('anchor-name', [...names.filter((each) => each !== this.anchored), name].join(', '))
+        }
+
+        this.anchored = name
+
+        if (rendered !== '') {
+            trigger.style.removeProperty('anchor-name')
+        }
+    },
+
+    /** Writes only what differs: the observer that calls this watches these same attributes. */
+    label() {
+        const control = this.control()
+
+        if (!control) {
+            return
+        }
+
+        const attributes = { 'aria-haspopup': 'menu', 'aria-controls': this.$refs.menu.id, 'aria-expanded': String(this.isOpen()) }
+
+        for (const [name, value] of Object.entries(attributes)) {
+            if (control.getAttribute(name) !== value) {
+                control.setAttribute(name, value)
             }
+        }
+    },
 
-            const attributes = { 'aria-haspopup': 'menu', 'aria-controls': this.$refs.menu.id, 'aria-expanded': String(this.isOpen()) }
+    isOpen() {
+        return this.$refs.menu.matches(':popover-open')
+    },
 
-            for (const [name, value] of Object.entries(attributes)) {
-                if (control.getAttribute(name) !== value) {
-                    control.setAttribute(name, value)
-                }
-            }
-        },
+    open(focus = 'first') {
+        this.label()
+        this.anchor()
 
-        isOpen() {
-            return this.$refs.menu.matches(':popover-open')
-        },
+        if (!this.isOpen()) {
+            this.$refs.menu.showPopover()
+            this.returnFocus = true
+        }
 
-        open(focus = 'first') {
-            this.label()
-            this.anchor()
+        this.control()?.setAttribute('aria-expanded', 'true')
 
-            if (!this.isOpen()) {
-                this.$refs.menu.showPopover()
-                this.returnFocus = true
-            }
-
-            this.control()?.setAttribute('aria-expanded', 'true')
+        // `false` opens without taking the focus: a submenu the pointer rested on belongs to the
+        // pointer, and taking the focus out from under the keyboard would be the wrong answer.
+        if (focus !== false) {
             this.focusItem(focus)
-        },
+        }
+    },
 
-        close() {
-            if (this.isOpen()) {
-                this.$refs.menu.hidePopover()
-            }
+    close() {
+        if (this.isOpen()) {
+            this.$refs.menu.hidePopover()
+        }
 
-            this.control()?.setAttribute('aria-expanded', 'false')
-        },
+        this.control()?.setAttribute('aria-expanded', 'false')
+    },
 
-        toggle(focus = 'first') {
-            if (this.isOpen()) {
+    toggle(focus = 'first') {
+        if (this.isOpen()) {
+            this.close()
+        } else if (performance.now() - this.closedAt > REOPEN_GUARD_MS) {
+            this.open(focus)
+        }
+    },
+
+    /**
+     * Every item of *this* menu, disabled ones included: M3 keeps a disabled item focusable
+     * ("disabled items can still receive focus, just aren't selectable") so a person reading the
+     * menu with the keyboard learns that it exists. activate() is where the refusal lives.
+     *
+     * An open submenu is a popover of its own nested in this one, and its rows are its: the
+     * nearest popover around a row says which menu the arrow keys should find it in.
+     */
+    items() {
+        return [...this.$refs.menu.querySelectorAll(ITEMS)].filter((item) => item.closest('[popover]') === this.$refs.menu)
+    },
+
+    /** The menu scrolls when it is too long for the window, so the item taken has to be shown. */
+    focusItem(which) {
+        const items = this.items()
+
+        this.reach(which === 'last' ? items.at(-1) : items[0])
+    },
+
+    reach(item) {
+        item?.focus()
+        item?.scrollIntoView({ block: 'nearest' })
+    },
+
+    navigate(event) {
+        const items = this.items()
+        const current = items.indexOf(document.activeElement)
+
+        const move = (index) => {
+            event.preventDefault()
+            this.reach(items[(index + items.length) % items.length])
+        }
+
+        switch (event.key) {
+            case 'ArrowDown':
+                return move(current + 1)
+            case 'ArrowUp':
+                return move(current < 0 ? items.length - 1 : current - 1)
+            case 'Home':
+                return move(0)
+            case 'End':
+                return move(items.length - 1)
+            case 'Escape':
+                this.returnFocus = true
+
+                return
+            case 'Tab':
+                this.returnFocus = false
                 this.close()
-            } else if (performance.now() - this.closedAt > REOPEN_GUARD_MS) {
-                this.open(focus)
-            }
-        },
 
-        /**
-         * Every item, disabled ones included: M3 keeps a disabled item focusable ("disabled items
-         * can still receive focus, just aren't selectable") so a person reading the menu with the
-         * keyboard learns that it exists. activate() is where the refusal lives.
-         */
-        items() {
-            return [...this.$refs.menu.querySelectorAll(ITEMS)]
-        },
+                return
+        }
 
-        /** The menu scrolls when it is too long for the window, so the item taken has to be shown. */
-        focusItem(which) {
-            const items = this.items()
+        // Typeahead: a printable letter moves to the next item whose label starts with it.
+        if (event.key.length === 1 && !event.ctrlKey && !event.metaKey && !event.altKey) {
+            const letter = event.key.toLowerCase()
+            const ordered = [...items.slice(current + 1), ...items.slice(0, current + 1)]
+            const match = ordered.find((item) => item.textContent.trim().toLowerCase().startsWith(letter))
 
-            this.reach(which === 'last' ? items.at(-1) : items[0])
-        },
-
-        reach(item) {
-            item?.focus()
-            item?.scrollIntoView({ block: 'nearest' })
-        },
-
-        navigate(event) {
-            const items = this.items()
-            const current = items.indexOf(document.activeElement)
-
-            const move = (index) => {
+            if (match) {
                 event.preventDefault()
-                this.reach(items[(index + items.length) % items.length])
+                this.reach(match)
             }
+        }
+    },
 
-            switch (event.key) {
-                case 'ArrowDown':
-                    return move(current + 1)
-                case 'ArrowUp':
-                    return move(current < 0 ? items.length - 1 : current - 1)
-                case 'Home':
-                    return move(0)
-                case 'End':
-                    return move(items.length - 1)
-                case 'Escape':
+    activate(event) {
+        const item = event.target.closest(ITEMS)
+
+        if (!item || item.getAttribute('aria-disabled') === 'true' || item.hasAttribute('data-keep-open')) {
+            return
+        }
+
+        this.close()
+    },
+
+    listen(target, type, handler) {
+        target.addEventListener(type, handler)
+        this.listeners.push(() => target.removeEventListener(type, handler))
+    },
+
+    destroy() {
+        this.listeners.forEach((remove) => remove())
+    },
+})
+
+document.addEventListener('alpine:init', () => {
+    window.Alpine.data('materialMenu', menu)
+
+    window.Alpine.data('materialSubmenu', () => {
+        const base = menu()
+
+        return {
+            ...base,
+            hoverTimer: null,
+
+            /** The item is the menu button, and the server named it: nothing has to be moved. */
+            control() {
+                return this.$refs.trigger
+            },
+
+            anchor() {},
+
+            navigate(event) {
+                // APG: Left closes a submenu and puts the focus back on the item that opened it.
+                // Escape does the same through the browser's own light dismiss, which the `toggle`
+                // listener follows with the focus.
+                if (event.key === 'ArrowLeft') {
+                    event.preventDefault()
                     this.returnFocus = true
+                    this.close()
+                    this.control()?.focus()
 
                     return
-                case 'Tab':
+                }
+
+                base.navigate.call(this, event)
+            },
+
+            /** Hover opens a submenu only where hovering means something, and never on a first tap. */
+            fine(event) {
+                return (event === undefined || event.pointerType !== 'touch') && window.matchMedia('(hover: hover) and (pointer: fine)').matches
+            },
+
+            hover(event) {
+                if (!this.fine(event)) {
+                    return
+                }
+
+                clearTimeout(this.hoverTimer)
+                this.hoverTimer = setTimeout(() => this.open(false), HOVER_OPEN_MS)
+            },
+
+            /**
+             * The submenu is a DOM child of the item's wrapper, so crossing into it is not a leave;
+             * a pointer that really left closes it, unless the keyboard has since taken it over.
+             */
+            unhover() {
+                clearTimeout(this.hoverTimer)
+
+                if (!this.fine()) {
+                    return
+                }
+
+                this.hoverTimer = setTimeout(() => {
+                    if (this.$el.contains(document.activeElement)) {
+                        return
+                    }
+
                     this.returnFocus = false
                     this.close()
+                }, HOVER_CLOSE_MS)
+            },
 
-                    return
-            }
-
-            // Typeahead: a printable letter moves to the next item whose label starts with it.
-            if (event.key.length === 1 && !event.ctrlKey && !event.metaKey && !event.altKey) {
-                const letter = event.key.toLowerCase()
-                const ordered = [...items.slice(current + 1), ...items.slice(0, current + 1)]
-                const match = ordered.find((item) => item.textContent.trim().toLowerCase().startsWith(letter))
-
-                if (match) {
-                    event.preventDefault()
-                    this.reach(match)
-                }
-            }
-        },
-
-        activate(event) {
-            const item = event.target.closest(ITEMS)
-
-            if (!item || item.getAttribute('aria-disabled') === 'true' || item.hasAttribute('data-keep-open')) {
-                return
-            }
-
-            this.close()
-        },
-
-        listen(target, type, handler) {
-            target.addEventListener(type, handler)
-            this.listeners.push(() => target.removeEventListener(type, handler))
-        },
-
-        destroy() {
-            this.listeners.forEach((remove) => remove())
-        },
-    }))
+            destroy() {
+                clearTimeout(this.hoverTimer)
+                base.destroy.call(this)
+            },
+        }
+    })
 })
diff --git a/resources/views/components/menu-item.blade.php b/resources/views/components/menu-item.blade.php
index ec66e8fa..8ef4d9c5 100644
--- a/resources/views/components/menu-item.blade.php
+++ b/resources/views/components/menu-item.blade.php
@@ -13,6 +13,14 @@
      is there. `keep-open` leaves the menu open when it is activated — for a choice the person may
      want to change twice.
 
+     `submenu` turns the item into a menu of its own: the slot holds `<x-menu-item>`s instead of a
+     label, and they open in a second popover beside this one, on the item's end, flipping to its
+     start where the window has no room. The item says so — `aria-haspopup="menu"`,
+     `aria-expanded`, and a chevron at its end — and keeps the APG menu keyboard: Right, Enter or
+     Space open it on its first item, Left or Escape close it and come back here, and on a fine
+     pointer resting on the item opens it. Choosing anything inside closes the whole menu, as it
+     would from the outer list.
+
      `icon-class` is for an icon whose colour means something of its own, a sport's glyph in the
      sport's colour (`icon-class="text-sport-run"`). A colour there paints the icon, a selected
      item's too: the icon's own colour then carries no specificity, because which of two colour
@@ -41,12 +49,18 @@
     'badge' => null,
     'disabled' => false,
     'keepOpen' => false,
+    'submenu' => false,
 ])
 
 @php
     $isLink = filled($link);
     $tag = $isLink ? 'a' : 'button';
 
+    // A submenu's own popover, named like the menu's: a new id and a new anchor name with every
+    // render, matched through a morph by the key rather than by either of them.
+    $key = $submenu ? \Illuminate\Support\Str::lower(\Illuminate\Support\Str::random(10)) : null;
+    $anchor = $submenu ? "--material-submenu-{$key}" : null;
+
     $attributes = $attributes
         ->class([
             'group/item state-layer flex w-full min-h-12 cursor-pointer items-center gap-3 px-4 text-start outline-none',
@@ -64,12 +78,19 @@
             'aria-current' => $current ? 'page' : null,
             'aria-disabled' => $disabled ? 'true' : null,
             'tabindex' => '-1',
+            'x-ref' => $submenu ? 'trigger' : null,
+            'style' => $submenu ? "anchor-name: {$anchor}" : null,
+            'aria-haspopup' => $submenu ? 'menu' : null,
+            'aria-expanded' => $submenu ? 'false' : null,
+            'aria-controls' => $submenu ? "material-submenu-{$key}" : null,
+            'x-on:click' => $submenu ? "toggle('first')" : null,
             'type' => $isLink ? null : 'button',
             'href' => $isLink ? $link : null,
             'target' => $isLink && $external ? '_blank' : null,
             'rel' => $isLink && $external ? 'noopener' : null,
             'wire:navigate' => $isLink && ! $external && ! $noWireNavigate && ! $attributes->has('wire:navigate') ? true : null,
-            'data-keep-open' => $keepOpen ? true : null,
+            // Opening a submenu is not choosing anything: the outer menu stays where it was.
+            'data-keep-open' => $keepOpen || $submenu ? true : null,
         ], fn ($value): bool => $value !== null));
 
     $iconInk = match (true) {
@@ -88,13 +109,21 @@
     };
 @endphp
 
+@if ($submenu)
+    <div x-data="materialSubmenu"
+        x-on:keydown.right.prevent.stop="open('first')"
+        x-on:pointerenter="hover($event)"
+        x-on:pointerleave="unhover()"
+    >
+@endif
+
 <{{ $tag }} {{ $attributes }}>
     @if ($icon)
         <x-livewire-material::icon :name="$icon" optical="20" :filled="$selected === true || $current" :class="$leadingIcon" />
     @endif
 
     <span class="min-w-0 flex-1">
-        <span class="block truncate type-body-lg">{{ $label ?? $slot }}</span>
+        <span class="block truncate type-body-lg">{{ $submenu ? $label : ($label ?? $slot) }}</span>
 
         @if ($description)
             <span @class(['block type-body-md', $iconInk])>{{ $description }}</span>
@@ -110,8 +139,31 @@
 
     @if ($iconRight)
         <x-livewire-material::icon :name="$iconRight" optical="20" :class="'size-5 '.$iconInk" />
+    @elseif ($submenu)
+        {{-- M3's submenu marker: it points the way the list opens, and turns over in an RTL page. --}}
+        <x-livewire-material::icon name="chevron_right" optical="20" :class="'size-5 rtl:-scale-x-100 '.$iconInk" />
     @elseif ($selected === true)
         {{-- The third cue M3 recommends, so a chosen item is not told by colour and shape alone. --}}
         <x-livewire-material::icon name="check" optical="20" :class="'size-5 '.$iconInk" />
     @endif
 </{{ $tag }}>
+
+@if ($submenu)
+        <div
+            x-ref="menu"
+            {{ new \Illuminate\View\ComponentAttributeBag(['wire:key' => 'material-submenu-'.substr(md5((string) $label), 0, 10)]) }}
+            id="material-submenu-{{ $key }}"
+            popover="auto"
+            role="menu"
+            data-submenu
+            aria-label="{{ $label }}"
+            tabindex="-1"
+            style="position-anchor: {{ $anchor }}"
+            x-on:keydown.stop="navigate($event)"
+            x-on:click="activate($event)"
+            class="m-0 mx-1 min-w-28 max-w-70 max-h-[min(18rem,calc(100dvh-2rem))] origin-top overflow-y-auto border-0 p-1 rounded-corner-lg shadow-elevation-2 popover-transition [inset:auto] [position-area:inline-end_span-block-end] [position-try-fallbacks:flip-inline]"
+        >
+            {{ $slot }}
+        </div>
+    </div>
+@endif
diff --git a/resources/views/components/menu.blade.php b/resources/views/components/menu.blade.php
index 50fc9dae..e86fbec6 100644
--- a/resources/views/components/menu.blade.php
+++ b/resources/views/components/menu.blade.php
@@ -69,6 +69,8 @@
         id="material-menu-{{ $key }}"
         popover="auto"
         role="menu"
+        data-menu
+        @if ($vibrant) data-vibrant @endif
         @if ($label) aria-label="{{ $label }}" @endif
         tabindex="-1"
         style="position-anchor: {{ $anchor }}"
diff --git a/resources/views/showcase/sections/menus.blade.php b/resources/views/showcase/sections/menus.blade.php
index 1bb3e727..446a9516 100644
--- a/resources/views/showcase/sections/menus.blade.php
+++ b/resources/views/showcase/sections/menus.blade.php
@@ -36,6 +36,30 @@
                 <x-menu-item label="Upload a folder" icon="drive_folder_upload" />
             </x-menu>
             BLADE,
+        'Submenus' => <<<'BLADE'
+            <x-menu label="Share actions">
+                <x-slot:trigger>
+                    <x-button label="Share" icon="share" variant="tonal" />
+                </x-slot:trigger>
+
+                <x-menu-item label="Copy link" icon="content_copy" shortcut="⌘C" />
+                <x-menu-item label="Send to" icon="send" submenu>
+                    <x-menu-item label="A person" icon="person" />
+                    <x-menu-item label="A team" icon="group" />
+                    <x-menu-item label="Somewhere else" icon="more_horiz" submenu>
+                        <x-menu-item label="Slack" icon="chat" />
+                        <x-menu-item label="Email" icon="mail" />
+                    </x-menu-item>
+                </x-menu-item>
+                <x-menu-item label="Export as" icon="download" submenu>
+                    <x-menu-item label="ZIP" icon="folder_zip" />
+                    <x-menu-item label="PDF" icon="picture_as_pdf" />
+                    <x-menu-item label="CSV" icon="table" disabled />
+                </x-menu-item>
+                <x-menu-separator />
+                <x-menu-item label="Delete" icon="delete" />
+            </x-menu>
+            BLADE,
         'Icons in their own colour' => <<<'BLADE'
             <x-menu label="New plan">
                 <x-slot:trigger>
@@ -56,7 +80,8 @@
 
     <p class="max-w-3xl type-body-md text-on-surface-variant">
         <code>&lt;x-menu&gt;</code> with <code>&lt;x-menu-item&gt;</code>, <code>&lt;x-menu-group&gt;</code> and <code>&lt;x-menu-separator&gt;</code>.
-        Open one with the keyboard too: arrows, Home, End, a letter, Escape.
+        Open one with the keyboard too: arrows, Home, End, a letter, Escape. A <code>submenu</code> item opens a second list beside it
+        &mdash; Right to enter it, Left to come back.
     </p>
 
     @foreach ($examples as $title => $code)
diff --git a/tests/Feature/Components/MenuTest.php b/tests/Feature/Components/MenuTest.php
index 44ec425b..19c9c936 100644
--- a/tests/Feature/Components/MenuTest.php
+++ b/tests/Feature/Components/MenuTest.php
@@ -117,3 +117,51 @@ it('adds icon-class to the leading icon, over its own colour but not over disabl
         ->and((string) $this->blade('<x-menu-item label="Next" icon-right="chevron_right" icon-class="text-sport-run" />'))
         ->not->toContain('text-sport-run');
 });
+
+it('opens a submenu beside the item that holds it', function () {
+    $html = (string) $this->blade(<<<'BLADE'
+        <x-menu-item label="Send to" icon="send" submenu>
+            <x-menu-item label="A person" icon="person" />
+        </x-menu-item>
+        BLADE);
+
+    preg_match('/anchor-name: (--material-submenu-([a-z0-9]+))/', $html, $anchor);
+
+    expect($anchor)->not->toBeEmpty()
+        ->and($html)
+        ->toContain('x-data="materialSubmenu"')
+        ->toContain('x-on:keydown.right.prevent.stop="open(\'first\')"')
+        ->toContain('x-on:pointerenter="hover($event)"')
+        ->toContain('aria-haspopup="menu"')
+        ->toContain('aria-expanded="false"')
+        ->toContain("aria-controls=\"material-submenu-{$anchor[2]}\"")
+        ->toContain("id=\"material-submenu-{$anchor[2]}\"")
+        ->toContain("position-anchor: {$anchor[1]}")
+        ->toContain('data-submenu')
+        ->toContain('aria-label="Send to"')
+        ->toContain('[position-area:inline-end_span-block-end]')
+        ->toContain('[position-try-fallbacks:flip-inline]')
+        // Opening a submenu chooses nothing, so the menu around it stays where it was.
+        ->toContain('data-keep-open')
+        ->toContain('A person');
+});
+
+it('marks a submenu item with a chevron instead of a tick', function () {
+    $chevron = trim((string) file_get_contents(__DIR__.'/../../../resources/svg/symbols/outlined-20/chevron_right.svg'));
+    $chevron = substr($chevron, (int) strpos($chevron, '><') + 1);
+
+    expect((string) $this->blade('<x-menu-item label="Export as" submenu><x-menu-item label="ZIP" /></x-menu-item>'))
+        ->toContain($chevron)
+        ->toContain('rtl:-scale-x-100')
+        ->and((string) $this->blade('<x-menu-item label="Export as" icon-right="download" submenu><x-menu-item label="ZIP" /></x-menu-item>'))
+        ->not->toContain($chevron);
+});
+
+it('tells a vibrant menu apart, so the submenus inside it take the same container', function () {
+    expect((string) $this->blade('<x-menu vibrant><x-slot:trigger><button>x</button></x-slot:trigger></x-menu>'))
+        ->toContain('data-menu')
+        ->toContain('data-vibrant')
+        ->and((string) $this->blade('<x-menu><x-slot:trigger><button>x</button></x-slot:trigger></x-menu>'))
+        ->toContain('data-menu')
+        ->not->toContain('data-vibrant');
+});