diff --git a/goldens/cdk/overlay/index.api.md b/goldens/cdk/overlay/index.api.md
index e5c474f19cbf..d0acaf6c780b 100644
--- a/goldens/cdk/overlay/index.api.md
+++ b/goldens/cdk/overlay/index.api.md
@@ -394,6 +394,7 @@ export class OverlayConfig {
     direction?: Direction | Directionality;
     disableAnimations?: boolean;
     disposeOnNavigation?: boolean;
+    eventPredicate?: (event: Event) => boolean;
     hasBackdrop?: boolean;
     height?: number | string;
     maxHeight?: number | string;
@@ -501,6 +502,7 @@ export class OverlayRef implements PortalOutlet {
     detachBackdrop(): void;
     detachments(): Observable<void>;
     dispose(): void;
+    get eventPredicate(): ((event: Event) => boolean) | null;
     getConfig(): OverlayConfig;
     getDirection(): Direction;
     hasAttached(): boolean;
diff --git a/src/cdk/overlay/dispatchers/base-overlay-dispatcher.ts b/src/cdk/overlay/dispatchers/base-overlay-dispatcher.ts
index 9c4c28490271..4d56a65ef244 100644
--- a/src/cdk/overlay/dispatchers/base-overlay-dispatcher.ts
+++ b/src/cdk/overlay/dispatchers/base-overlay-dispatcher.ts
@@ -8,6 +8,7 @@
 
 import {Injectable, OnDestroy, inject, DOCUMENT} from '@angular/core';
 import type {OverlayRef} from '../overlay-ref';
+import {Subject} from 'rxjs';
 
 /**
  * Service for dispatching events that land on the body to appropriate overlay ref,
@@ -53,4 +54,17 @@ export abstract class BaseOverlayDispatcher implements OnDestroy {
 
   /** Detaches the global event listener. */
   protected abstract detach(): void;
+
+  /** Determines whether an overlay is allowed to receive an event. */
+  protected canReceiveEvent<T>(overlayRef: OverlayRef, event: Event, stream: Subject<T>): boolean {
+    if (stream.observers.length < 1) {
+      return false;
+    }
+
+    if (overlayRef.eventPredicate) {
+      return overlayRef.eventPredicate(event);
+    }
+
+    return true;
+  }
 }
diff --git a/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.spec.ts b/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.spec.ts
index 8d4d378a4f02..a5b89112a693 100644
--- a/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.spec.ts
+++ b/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.spec.ts
@@ -187,6 +187,26 @@ describe('OverlayKeyboardDispatcher', () => {
     dispatchKeyboardEvent(document.body, 'keydown', ESCAPE);
     expect(appRef.tick).toHaveBeenCalledTimes(0);
   });
+
+  it('should not dispatch to overlay whose eventPredicate does not allow the event', () => {
+    const overlayOne = createOverlayRef(injector);
+    const overlayTwo = createOverlayRef(injector, {eventPredicate: () => false});
+    const overlayOneSpy = jasmine.createSpy('overlayOne keyboard event spy');
+    const overlayTwoSpy = jasmine.createSpy('overlayTwo keyboard event spy');
+
+    overlayOne.keydownEvents().subscribe(overlayOneSpy);
+    overlayTwo.keydownEvents().subscribe(overlayTwoSpy);
+
+    // Attach overlays
+    keyboardDispatcher.add(overlayOne);
+    keyboardDispatcher.add(overlayTwo);
+
+    dispatchKeyboardEvent(document.body, 'keydown', ESCAPE);
+
+    // Most recent overlay should receive event
+    expect(overlayOneSpy).toHaveBeenCalled();
+    expect(overlayTwoSpy).not.toHaveBeenCalled();
+  });
 });
 
 @Component({template: 'Hello'})
diff --git a/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.ts b/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.ts
index 82d8a9bb5604..b3b0e6aff9d6 100644
--- a/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.ts
+++ b/src/cdk/overlay/dispatchers/overlay-keyboard-dispatcher.ts
@@ -54,8 +54,9 @@ export class OverlayKeyboardDispatcher extends BaseOverlayDispatcher {
       // (e.g. for select and autocomplete). We skip overlays without keydown event subscriptions,
       // because we don't want overlays that don't handle keyboard events to block the ones below
       // them that do.
-      if (overlays[i]._keydownEvents.observers.length > 0) {
-        this._ngZone.run(() => overlays[i]._keydownEvents.next(event));
+      const overlayRef = overlays[i];
+      if (this.canReceiveEvent(overlayRef, event, overlayRef._keydownEvents)) {
+        this._ngZone.run(() => overlayRef._keydownEvents.next(event));
         break;
       }
     }
diff --git a/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.spec.ts b/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.spec.ts
index b9ff3647b097..0ce18f25c739 100644
--- a/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.spec.ts
+++ b/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.spec.ts
@@ -334,6 +334,34 @@ describe('OverlayOutsideClickDispatcher', () => {
     thirdOverlayRef.dispose();
   });
 
+  it('should not dispatch to overlays whose eventPredicate does not allow the event', () => {
+    const eventPredicate = () => false;
+    const overlayOne = createOverlayRef(injector, {eventPredicate});
+    overlayOne.attach(new ComponentPortal(TestComponent));
+    const overlayTwo = createOverlayRef(injector, {eventPredicate});
+    overlayTwo.attach(new ComponentPortal(TestComponent));
+
+    const overlayOneSpy = jasmine.createSpy('overlayOne mouse click event spy');
+    const overlayTwoSpy = jasmine.createSpy('overlayTwo mouse click event spy');
+
+    overlayOne.outsidePointerEvents().subscribe(overlayOneSpy);
+    overlayTwo.outsidePointerEvents().subscribe(overlayTwoSpy);
+
+    outsideClickDispatcher.add(overlayOne);
+    outsideClickDispatcher.add(overlayTwo);
+
+    const button = document.createElement('button');
+    document.body.appendChild(button);
+    button.click();
+
+    expect(overlayOneSpy).not.toHaveBeenCalled();
+    expect(overlayTwoSpy).not.toHaveBeenCalled();
+
+    button.remove();
+    overlayOne.dispose();
+    overlayTwo.dispose();
+  });
+
   describe('change detection behavior', () => {
     it('should not run change detection if there is no portal attached to the overlay', () => {
       spyOn(appRef, 'tick');
diff --git a/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.ts b/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.ts
index 5077f69cfe0d..710a33438212 100644
--- a/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.ts
+++ b/src/cdk/overlay/dispatchers/overlay-outside-click-dispatcher.ts
@@ -107,7 +107,13 @@ export class OverlayOutsideClickDispatcher extends BaseOverlayDispatcher {
     // the loop.
     for (let i = overlays.length - 1; i > -1; i--) {
       const overlayRef = overlays[i];
-      if (overlayRef._outsidePointerEvents.observers.length < 1 || !overlayRef.hasAttached()) {
+      const outsidePointerEvents = overlayRef._outsidePointerEvents;
+
+      if (
+        // TODO(crisbeto): this should move into `canReceiveEvent` but may be breaking.
+        !overlayRef.hasAttached() ||
+        !this.canReceiveEvent(overlayRef, event, outsidePointerEvents)
+      ) {
         continue;
       }
 
@@ -121,7 +127,6 @@ export class OverlayOutsideClickDispatcher extends BaseOverlayDispatcher {
         break;
       }
 
-      const outsidePointerEvents = overlayRef._outsidePointerEvents;
       /** @breaking-change 14.0.0 _ngZone will be required. */
       if (this._ngZone) {
         this._ngZone.run(() => outsidePointerEvents.next(event));
diff --git a/src/cdk/overlay/overlay-config.ts b/src/cdk/overlay/overlay-config.ts
index c49ed9c1eb2b..e0ec3af1fec2 100644
--- a/src/cdk/overlay/overlay-config.ts
+++ b/src/cdk/overlay/overlay-config.ts
@@ -67,6 +67,12 @@ export class OverlayConfig {
    */
   usePopover?: boolean;
 
+  /**
+   * Function that determines if the overlay should receive a specific
+   * event or if the event should go to the next overlay in the stack.
+   */
+  eventPredicate?: (event: Event) => boolean;
+
   constructor(config?: OverlayConfig) {
     if (config) {
       // Use `Iterable` instead of `Array` because TypeScript, as of 3.6.3,
diff --git a/src/cdk/overlay/overlay-ref.ts b/src/cdk/overlay/overlay-ref.ts
index f60a8a72ad3c..040efd324f95 100644
--- a/src/cdk/overlay/overlay-ref.ts
+++ b/src/cdk/overlay/overlay-ref.ts
@@ -109,6 +109,14 @@ export class OverlayRef implements PortalOutlet {
     return this._host;
   }
 
+  /**
+   * Function that determines if this overlay should receive a specific event.
+   */
+  get eventPredicate(): ((event: Event) => boolean) | null {
+    // Note: the safe read here is redundant, but some internal tests mock out the overlay ref.
+    return this._config?.eventPredicate || null;
+  }
+
   attach<T>(portal: ComponentPortal<T>): ComponentRef<T>;
   attach<T>(portal: TemplatePortal<T>): EmbeddedViewRef<T>;
   attach(portal: any): any;
diff --git a/src/material/tooltip/tooltip.ts b/src/material/tooltip/tooltip.ts
index 885ae2d08cb8..221b4199c4e8 100644
--- a/src/material/tooltip/tooltip.ts
+++ b/src/material/tooltip/tooltip.ts
@@ -543,6 +543,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
       panelClass: this._overlayPanelClass ? [...this._overlayPanelClass, panelClass] : panelClass,
       scrollStrategy: this._injector.get(MAT_TOOLTIP_SCROLL_STRATEGY)(),
       disableAnimations: this._animationsDisabled,
+      eventPredicate: this._overlayEventPredicate,
     });
 
     this._updatePosition(this._overlayRef);
@@ -561,11 +562,10 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
       .keydownEvents()
       .pipe(takeUntil(this._destroyed))
       .subscribe(event => {
-        if (this._isTooltipVisible() && event.keyCode === ESCAPE && !hasModifierKey(event)) {
-          event.preventDefault();
-          event.stopPropagation();
-          this._ngZone.run(() => this.hide(0));
-        }
+        // Note: we don't check the `keyCode` since it's covered by the `eventPredicate` above.
+        event.preventDefault();
+        event.stopPropagation();
+        this._ngZone.run(() => this.hide(0));
       });
 
     if (this._defaultOptions?.disableTooltipInteractivity) {
@@ -935,6 +935,18 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
       );
     }
   }
+
+  /** Determines which events should be routed to the tooltip overlay. */
+  private _overlayEventPredicate = (event: Event) => {
+    if (event.type === 'keydown') {
+      return (
+        this._isTooltipVisible() &&
+        (event as KeyboardEvent).keyCode === ESCAPE &&
+        !hasModifierKey(event as KeyboardEvent)
+      );
+    }
+    return true;
+  };
 }
 
 /**