diff --git a/packages/daemon/src/daemon.js b/packages/daemon/src/daemon.js
index f66407a7ca..8db27f75ff 100644
--- a/packages/daemon/src/daemon.js
+++ b/packages/daemon/src/daemon.js
@@ -14,6 +14,7 @@ import { assertPetName } from './pet-name.js';
 import { makeContextMaker } from './context.js';
 import { parseFormulaIdentifier } from './formula-identifier.js';
 import { makeMutex } from './mutex.js';
+import { makeWeakMultimap } from './weak-multimap.js';
 
 const delay = async (ms, cancelled) => {
   // Do not attempt to set up a timer if already cancelled.
@@ -96,12 +97,15 @@ const makeDaemonCore = async (
    * @type {Map<string, import('./types.js').Controller>}
    */
   const controllerForFormulaIdentifier = new Map();
+
   /**
    * Reverse look-up, for answering "what is my name for this near or far
    * reference", and not for "what is my name for this promise".
-   * @type {WeakMap<object, string>}
+   * @type {import('./types.js').WeakMultimap<Record<string | symbol, unknown>, string>}
    */
-  const formulaIdentifierForRef = new WeakMap();
+  const formulaIdentifierForRef = makeWeakMultimap();
+
+  /** @type {import('./types.js').WeakMultimap<Record<string | symbol, unknown>, string>['get']} */
   const getFormulaIdentifierForRef = ref => formulaIdentifierForRef.get(ref);
 
   /**
@@ -586,7 +590,7 @@ const makeDaemonCore = async (
       context,
       external: E.get(partial).external.then(value => {
         if (typeof value === 'object' && value !== null) {
-          formulaIdentifierForRef.set(value, formulaIdentifier);
+          formulaIdentifierForRef.add(value, formulaIdentifier);
         }
         return value;
       }),
@@ -669,7 +673,7 @@ const makeDaemonCore = async (
       // Release the value to the public only after ensuring
       // we can reverse-lookup its nonce.
       if (typeof value === 'object' && value !== null) {
-        formulaIdentifierForRef.set(value, formulaIdentifier);
+        formulaIdentifierForRef.add(value, formulaIdentifier);
       }
       return value;
     });
diff --git a/packages/daemon/src/types.d.ts b/packages/daemon/src/types.d.ts
index 90d48ebee0..05c4dbae08 100644
--- a/packages/daemon/src/types.d.ts
+++ b/packages/daemon/src/types.d.ts
@@ -359,7 +359,7 @@ export interface Mail {
   remove: PetStore['remove'];
   list: PetStore['list'];
   identifyLocal: PetStore['identifyLocal'];
-  reverseLookup: PetStore['reverseLookup'];
+  reverseLookup(value: unknown): Array<string>;
   // Extended methods:
   lookup(...petNamePath: string[]): Promise<unknown>;
   listSpecial(): Array<string>;
@@ -637,8 +637,44 @@ export type DaemonicPowers = {
   control: DaemonicControlPowers;
 };
 
-type Mutex = {
+export type Mutex = {
   lock: () => Promise<void>;
   unlock: () => void;
   enqueue: <T>(asyncFn?: () => Promise<T>) => Promise<T>;
 };
+
+/**
+ * A multimap backed by a WeakMap. Keys must be objects.
+ */
+export type WeakMultimap<K extends WeakKey, V> = {
+  /**
+   * @param key - The key to add a value for.
+   * @param value - The value to add.
+   */
+  add(key: K, value: V): void;
+
+  /**
+   * @param key - The key whose value to delete.
+   * @param value - The value to delete.
+   * @returns `true` if the key was found and the value was deleted, `false` otherwise.
+   */
+  delete(key: K, value: V): boolean;
+
+  /**
+   * @param key - The key whose values to delete
+   * @returns `true` if the key was found and its values were deleted, `false` otherwise.
+   */
+  deleteAll(key: K): boolean;
+
+  /**
+   * @param key - The key whose first value to retrieve
+   * @returns The first value associated with the key.
+   */
+  get(key: K): V | undefined;
+
+  /**
+   * @param key - The key whose values to retrieve.
+   * @returns An array of all values associated with the key.
+   */
+  getAll(key: K): V[];
+};
diff --git a/packages/daemon/src/weak-multimap.js b/packages/daemon/src/weak-multimap.js
new file mode 100644
index 0000000000..5051a03685
--- /dev/null
+++ b/packages/daemon/src/weak-multimap.js
@@ -0,0 +1,35 @@
+/**
+ * @returns {import('./types.js').WeakMultimap<WeakKey, any>}
+ */
+export const makeWeakMultimap = () => {
+  /** @type {WeakMap<WeakKey, Set<unknown>>} */
+  const map = new WeakMap();
+  return {
+    add: (ref, formulaIdentifier) => {
+      let set = map.get(ref);
+      if (set === undefined) {
+        set = new Set();
+        map.set(ref, set);
+      }
+      set.add(formulaIdentifier);
+    },
+
+    delete: (ref, formulaIdentifier) => {
+      const set = map.get(ref);
+      if (set !== undefined) {
+        const result = set.delete(formulaIdentifier);
+        if (set.size === 0) {
+          map.delete(ref);
+        }
+        return result;
+      }
+      return false;
+    },
+
+    deleteAll: ref => map.delete(ref),
+
+    get: ref => map.get(ref)?.keys().next().value,
+
+    getAll: ref => Array.from(map.get(ref) ?? []),
+  };
+};
diff --git a/packages/daemon/test/test-weak-multimap.js b/packages/daemon/test/test-weak-multimap.js
new file mode 100644
index 0000000000..e985d7254b
--- /dev/null
+++ b/packages/daemon/test/test-weak-multimap.js
@@ -0,0 +1,82 @@
+import test from 'ava';
+import { makeWeakMultimap } from '../src/weak-multimap.js';
+
+test('add and get', t => {
+  const multimap = makeWeakMultimap();
+  const ref = {};
+  const value = 'foo';
+
+  multimap.add(ref, value);
+  t.is(multimap.get(ref), value);
+
+  // Adding a value for a key should be idempotent.
+  multimap.add(ref, value);
+  t.is(multimap.get(ref), value);
+});
+
+test('add and get with multiple refs', t => {
+  const multimap = makeWeakMultimap();
+  const ref1 = {};
+  const ref2 = {};
+  const value1 = 'foo';
+  const value2 = 'bar';
+
+  multimap.add(ref1, value1);
+  multimap.add(ref1, value2);
+  multimap.add(ref2, value1);
+
+  t.is(multimap.get(ref1), value1);
+  t.deepEqual(multimap.getAll(ref1), [value1, value2]);
+  t.is(multimap.get(ref2), value1);
+  t.deepEqual(multimap.getAll(ref2), [value1]);
+});
+
+test('getAll', t => {
+  const multimap = makeWeakMultimap();
+  const ref = {};
+  const value1 = 'foo';
+  const value2 = 'bar';
+
+  multimap.add(ref, value1);
+  multimap.add(ref, value2);
+  t.deepEqual(multimap.getAll(ref), [value1, value2]);
+
+  // Adding a value for a key should be idempotent.
+  multimap.add(ref, value1);
+  multimap.add(ref, value2);
+  t.deepEqual(multimap.getAll(ref), [value1, value2]);
+});
+
+test('delete', t => {
+  const multimap = makeWeakMultimap();
+  const ref = {};
+  const value = 'foo';
+
+  multimap.add(ref, value);
+
+  t.is(multimap.get(ref), value);
+  t.is(multimap.delete(ref, value), true);
+  t.is(multimap.get(ref), undefined);
+
+  // Deleting should be idempotent.
+  t.is(multimap.delete(ref, value), false);
+  t.is(multimap.get(ref), undefined);
+});
+
+test('deleteAll', t => {
+  const multimap = makeWeakMultimap();
+  const ref = {};
+  const value1 = 'foo';
+  const value2 = 'bar';
+
+  multimap.add(ref, value1);
+  multimap.add(ref, value2);
+
+  t.deepEqual(multimap.getAll(ref), [value1, value2]);
+  t.is(multimap.deleteAll(ref), true);
+  t.is(multimap.get(ref), undefined);
+
+  // Deleting should be idempotent.
+  t.is(multimap.deleteAll(ref), false);
+  t.is(multimap.get(ref), undefined);
+});