diff --git a/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.outside-press.test.tsx b/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.outside-press.test.tsx
new file mode 100644
index 00000000..071d4721
--- /dev/null
+++ b/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.outside-press.test.tsx
@@ -0,0 +1,141 @@
+import { Popover } from '@base-ui/react/popover'
+import { act, fireEvent, render, screen, waitFor } from '@testing-library/react'
+import userEvent from '@testing-library/user-event'
+import * as React from 'react'
+import { describe, expect, it } from 'vitest'
+import { DropdownMenu } from '../../../dropdown-menu/index.js'
+import { PopupMenuProviders } from '../components/providers.js'
+import { usePopupMenuRoot } from './use-popup-menu-root.js'
+
+function ExemptRoot(props: {
+  exempt: boolean
+  onRoot?: (root: ReturnType<typeof usePopupMenuRoot>) => void
+}) {
+  const hostRef = React.useRef<HTMLInputElement>(null)
+  const root = usePopupMenuRoot({
+    defaultOpen: true,
+    getDismissExemptElements: () => (props.exempt ? [hostRef.current] : []),
+  })
+  const open = root.store.useState('open')
+  props.onRoot?.(root)
+  return (
+    <>
+      <input ref={hostRef} data-testid="host" />
+      <button type="button" data-testid="elsewhere">
+        Elsewhere
+      </button>
+      <PopupMenuProviders
+        store={root.store}
+        menuTreeResolver={root.menuTreeResolver}
+        focusOwnerStore={root.focusOwnerStore}
+        openChainStore={root.openChainStore}
+        disabled={root.disabled}
+        depth={0}
+        closeAll={root.closeAll}
+        registerSurface={root.registerSurface}
+        menuType="dropdown"
+        externalFocus
+      >
+        <Popover.Root
+          open={open}
+          modal={false}
+          onOpenChange={(nextOpen, details) =>
+            root.handleOpenChange(
+              nextOpen,
+              details.reason as Parameters<typeof root.handleOpenChange>[1],
+              details.event,
+            )
+          }
+        >
+          <DropdownMenu.Portal>
+            <DropdownMenu.Positioner>
+              <DropdownMenu.Popup data-testid="popup">
+                <DropdownMenu.Surface>
+                  <DropdownMenu.List>
+                    <DropdownMenu.Item>Apple</DropdownMenu.Item>
+                  </DropdownMenu.List>
+                </DropdownMenu.Surface>
+              </DropdownMenu.Popup>
+            </DropdownMenu.Positioner>
+          </DropdownMenu.Portal>
+        </Popover.Root>
+      </PopupMenuProviders>
+    </>
+  )
+}
+
+describe('usePopupMenuRoot outside-press exemptions', () => {
+  it('stays open when an exempt element is pressed', async () => {
+    const user = userEvent.setup()
+    render(<ExemptRoot exempt />)
+    await screen.findByTestId('popup')
+
+    await user.click(screen.getByTestId('host'))
+    await new Promise((resolve) => setTimeout(resolve, 20))
+
+    expect(screen.getByTestId('popup')).toBeInTheDocument()
+  })
+
+  it('still closes when something else outside is pressed', async () => {
+    const user = userEvent.setup()
+    render(<ExemptRoot exempt />)
+    await screen.findByTestId('popup')
+
+    await user.click(screen.getByTestId('elsewhere'))
+
+    await waitFor(() =>
+      expect(screen.queryByTestId('popup')).not.toBeInTheDocument(),
+    )
+  })
+
+  it('closes on a press on the element when it is not exempt', async () => {
+    render(<ExemptRoot exempt={false} />)
+    await screen.findByTestId('popup')
+
+    fireEvent.pointerDown(screen.getByTestId('host'))
+
+    await waitFor(() =>
+      expect(screen.queryByTestId('popup')).not.toBeInTheDocument(),
+    )
+  })
+
+  describe('focus-out', () => {
+    function focusOut(target: Element, relatedTarget: Element | null) {
+      const event = new FocusEvent('focusout', { relatedTarget })
+      Object.defineProperty(event, 'target', { value: target })
+      return event
+    }
+
+    it('stays open when focus moves to an exempt element', async () => {
+      let root!: ReturnType<typeof usePopupMenuRoot>
+      render(<ExemptRoot exempt onRoot={(r) => (root = r)} />)
+      const popup = await screen.findByTestId('popup')
+
+      act(() => {
+        root.handleOpenChange(
+          false,
+          'focus-out',
+          focusOut(popup, screen.getByTestId('host')),
+        )
+      })
+
+      expect(root.store.state.open).toBe(true)
+    })
+
+    it('closes when focus leaves an exempt element for somewhere else', async () => {
+      let root!: ReturnType<typeof usePopupMenuRoot>
+      render(<ExemptRoot exempt onRoot={(r) => (root = r)} />)
+      await screen.findByTestId('popup')
+
+      act(() => {
+        root.handleOpenChange(
+          false,
+          'focus-out',
+          focusOut(screen.getByTestId('host'), screen.getByTestId('elsewhere')),
+        )
+      })
+
+      expect(root.store.state.open).toBe(false)
+    })
+  })
+})
diff --git a/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.ts b/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.ts
index 78c6cbf6..e3859d37 100644
--- a/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.ts
+++ b/packages/react/src/internal/popup-menu/hooks/use-popup-menu-root.ts
@@ -74,6 +74,14 @@ export interface UsePopupMenuRootParams {
    */
   closeOnOutsidePress?: 'click' | 'pointerdown'
 
+  /**
+   * Elements outside the menu that don't dismiss it (e.g. a suggestion menu's
+   * host input): pressing one, or moving focus from the menu to one, is not an
+   * outside press or a focus-out. Read when the event happens, so the returned
+   * elements may change over time.
+   */
+  getDismissExemptElements?: () => ReadonlyArray<Element | null | undefined>
+
   /**
    * Whether the menu should ignore user interaction.
    * Can be controlled declaratively via this prop, or imperatively via actionsRef.setDisabled().
@@ -152,6 +160,7 @@ export function usePopupMenuRoot(
     items: itemsProp,
     onHighlightChange,
     closeOnOutsidePress = 'pointerdown',
+    getDismissExemptElements,
     disabled: disabledProp = false,
     defaultDisabled = false,
     getResolvedId,
@@ -197,6 +206,14 @@ export function usePopupMenuRoot(
     ensureInputModalityTracking()
   }, [])
 
+  const getExemptElementsRef = React.useRef(getDismissExemptElements)
+  getExemptElementsRef.current = getDismissExemptElements
+  const isExemptNode = React.useCallback((node: unknown): boolean => {
+    if (!(node instanceof Node)) return false
+    const elements = getExemptElementsRef.current?.() ?? []
+    return elements.some((element) => element?.contains(node) ?? false)
+  }, [])
+
   // Track outside pointer events to distinguish outside-press from focus-out
   // When a pointerdown happens outside the menu, we store it so that if a
   // focus-out close happens immediately after, we can treat it as outside-press
@@ -322,6 +339,8 @@ export function usePopupMenuRoot(
     const handlePointerDown = (event: PointerEvent) => {
       const target = event.target as Element | null
       if (!target) return
+      // Presses on an exempt element (e.g. a host input) count as inside.
+      if (isExemptNode(target)) return
 
       // Check if the pointerdown is inside any part of the menu tree or its triggers
       // base-ui sets data-open on popups and data-popup-open on triggers
@@ -344,7 +363,7 @@ export function usePopupMenuRoot(
       document.removeEventListener('pointerdown', handlePointerDown, true)
       outsidePointerEventRef.current = null
     }
-  }, [isOpen, closeOnOutsidePress, disabled])
+  }, [isOpen, closeOnOutsidePress, disabled, isExemptNode])
 
   // Handle open state change
   const handleOpenChange = React.useCallback(
@@ -360,6 +379,19 @@ export function usePopupMenuRoot(
         return
       }
 
+      // A press on an exempt element, or focus moving to one, doesn't dismiss.
+      // Covers Base UI's own dismissal, which runs alongside our listener.
+      // For focus-out only the element gaining focus (`relatedTarget`) counts:
+      // `target` is the element losing it.
+      if (
+        !newOpen &&
+        ((reason === REASONS.outsidePress && isExemptNode(event?.target)) ||
+          (reason === REASONS.focusOut &&
+            isExemptNode((event as FocusEvent | undefined)?.relatedTarget)))
+      ) {
+        return
+      }
+
       store.setOpen(newOpen, reason, event)
       // Clear focus ownership and open chain when menu closes
       if (!newOpen) {
@@ -367,7 +399,7 @@ export function usePopupMenuRoot(
         openChainStore.clear()
       }
     },
-    [store, focusOwnerStore, openChainStore, disabled],
+    [store, focusOwnerStore, openChainStore, disabled, isExemptNode],
   )
 
   // Memoize listbox wiring config