diff --git a/lib/internal/util/comparisons.js b/lib/internal/util/comparisons.js
index 535c3484bfea..7176c319e3bc 100644
--- a/lib/internal/util/comparisons.js
+++ b/lib/internal/util/comparisons.js
@@ -4,6 +4,7 @@ const {
   Array,
   ArrayBuffer,
   ArrayIsArray,
+  ArrayPrototypeFill,
   ArrayPrototypePush,
   BigInt,
   BigInt64Array,
@@ -638,6 +639,82 @@ function mapMightHaveLoosePrim(a, b, prim, item2, memo) {
   return !b.has(altValue) && innerDeepEqual(item1, item2, kLoose, memo);
 }
 
+function partialCollectionEquiv(a, b, memo, iterationType) {
+  const valuesA = [];
+  const valuesB = [];
+  // Primitive keys and members were handled by the caller. Shared Set members
+  // are already matched, but shared Map keys may have different values.
+  for (const value of a) {
+    const key = iterationType === kIsMap ? value[0] : value;
+    if (typeof key === 'object' && key !== null &&
+        (iterationType === kIsMap || !b.has(key))) {
+      ArrayPrototypePush(valuesA, value);
+    }
+  }
+  for (const value of iterationType === kIsMap ? b : b.values()) {
+    const key = iterationType === kIsMap ? value[0] : value;
+    if (typeof key === 'object' && key !== null &&
+        (iterationType === kIsMap || !a.has(key))) {
+      ArrayPrototypePush(valuesB, value);
+    }
+  }
+  if (valuesA.length < valuesB.length) {
+    return false;
+  }
+  const matched = new Uint32Array(valuesA.length);
+  const visited = new Uint32Array(valuesA.length);
+  const parents = new Uint32Array(valuesB.length);
+  const paths = new Uint32Array(valuesB.length);
+  const comparisons = ArrayPrototypeFill(new Array(valuesB.length), undefined);
+
+  // Partial matches can overlap. If greedy matching fails, find augmenting
+  // paths to reassign earlier matches, comparing each pair at most once.
+  for (let i = 0; i < valuesB.length; i++) {
+    const queue = [i];
+    let found = false;
+    for (let j = 0; j < queue.length && !found; j++) {
+      const current = queue[j];
+      const val2 = valuesB[current];
+      const results = comparisons[current] ??= new Uint8Array(valuesA.length);
+      for (let k = 0; k < valuesA.length; k++) {
+        if (visited[k] === i + 1) {
+          continue;
+        }
+        if (results[k] === 0) {
+          const val1 = valuesA[k];
+          const equal = iterationType === kIsMap ?
+            innerDeepEqual(val1[0], val2[0], kPartial, memo) &&
+              innerDeepEqual(val1[1], val2[1], kPartial, memo) :
+            innerDeepEqual(val1, val2, kPartial, memo);
+          results[k] = equal ? 2 : 1;
+        }
+        if (results[k] === 1) {
+          continue;
+        }
+        visited[k] = i + 1;
+        if (matched[k] === 0) {
+          matched[k] = current + 1;
+          let previous = current;
+          while (previous !== i) {
+            matched[paths[previous]] = parents[previous] + 1;
+            previous = parents[previous];
+          }
+          found = true;
+          break;
+        }
+        const next = matched[k] - 1;
+        parents[next] = current;
+        paths[next] = k;
+        ArrayPrototypePush(queue, next);
+      }
+    }
+    if (!found) {
+      return false;
+    }
+  }
+  return true;
+}
+
 function partialObjectSetEquiv(array, a, b, mode, memo) {
   let aPos = 0;
   let direction = 1;
@@ -745,7 +822,13 @@ function compareSmallSets(a, b, val, iteratorB, mode, memo) {
       return true;
     }
     const secondA = iteratorA.next().value;
-    return b.has(secondA) || innerDeepEqual(secondA, iteratorB.next().value, mode, memo);
+    if (b.has(secondA)) {
+      return true;
+    }
+    const secondB = iteratorB.next().value;
+    return innerDeepEqual(secondA, secondB, mode, memo) ||
+      (mode === kPartial && innerDeepEqual(secondA, val, mode, memo) &&
+        (b.has(firstA) || innerDeepEqual(firstA, secondB, mode, memo)));
   }
   return a.size !== 1 && innerDeepEqual(iteratorA.next().value, val, mode, memo) && (
     b.size === 1 || // Partial mode
@@ -784,7 +867,8 @@ function setEquiv(a, b, mode, memo) {
     return true;
   }
   if (mode === kPartial) {
-    return partialObjectSetEquiv(array, a, b, mode, memo);
+    return partialObjectSetEquiv(array, a, b, mode, memo) ||
+      partialCollectionEquiv(a, b, memo, kIsSet);
   }
   return setObjectEquiv(array, a, b, mode, memo);
 }
@@ -932,7 +1016,8 @@ function mapEquiv(a, b, mode, memo) {
   }
 
   if (mode === kPartial) {
-    return partialObjectMapEquiv(array, a, b, mode, memo);
+    return partialObjectMapEquiv(array, a, b, mode, memo) ||
+      partialCollectionEquiv(a, b, memo, kIsMap);
   }
 
   return mapObjectEquiv(array, a, b, mode, memo);
diff --git a/test/parallel/test-assert-deep.js b/test/parallel/test-assert-deep.js
index 91faa7839854..7f5eeec93a6b 100644
--- a/test/parallel/test-assert-deep.js
+++ b/test/parallel/test-assert-deep.js
@@ -591,6 +591,37 @@ test('es6 Maps and Sets', () => {
   }
 });
 
+test('partial comparison of unordered Sets and Maps with overlapping entries', () => {
+  assertDeepAndStrictEqual(
+    new Set([[1, 2], [1]]),
+    new Set([[1], [1, 2]])
+  );
+  assertDeepAndStrictEqual(
+    new Set([[1, 2], [1], [3]]),
+    new Set([[1], [1, 2], [3]])
+  );
+  assertDeepAndStrictEqual(
+    new Set([{ a: 1, b: 1 }, { a: 1 }]),
+    new Set([{ a: 1 }, { a: 1, b: 1 }])
+  );
+  assertDeepAndStrictEqual(
+    new Map([[{ a: 1, b: 1 }, 1], [{ a: 1 }, 1]]),
+    new Map([[{ a: 1 }, 1], [{ a: 1, b: 1 }, 1]])
+  );
+});
+
+test('partial comparison of unordered Sets with circular entries', () => {
+  const actual = new Set([{ a: 1, b: 1 }, { a: 1 }, { a: 2 }]);
+  const expected = new Set([{ a: 1 }, { a: 1, b: 1 }, { a: 2 }]);
+  for (const value of actual) {
+    value.self = actual;
+  }
+  for (const value of expected) {
+    value.self = expected;
+  }
+  assertDeepAndStrictEqual(actual, expected);
+});
+
 test('GH-6416. Make sure circular refs do not throw', () => {
   const b = {};
   b.b = b;
diff --git a/test/parallel/test-util-isPartialDeepStrictEqual.js b/test/parallel/test-util-isPartialDeepStrictEqual.js
index 3b1ae08eb57f..3caa197c7d6a 100644
--- a/test/parallel/test-util-isPartialDeepStrictEqual.js
+++ b/test/parallel/test-util-isPartialDeepStrictEqual.js
@@ -38,6 +38,24 @@ test('util.isPartialDeepStrictEqual returns true with expected properties', () =
   );
 });
 
+test('util.isPartialDeepStrictEqual matches unordered collections with overlapping entries', () => {
+  const shared = { c: 3 };
+  assert.strictEqual(
+    util.isPartialDeepStrictEqual(
+      new Set([null, shared, 1, [1, 2, 3], [1, 3], [4]]),
+      new Set([null, shared, 1, [1], [1, 2]]),
+    ),
+    true,
+  );
+  assert.strictEqual(
+    util.isPartialDeepStrictEqual(
+      new Map([[null, 0], [1, 1], [shared, [1, 2, 3]], [{}, [1, 3]]]),
+      new Map([[null, 0], [1, 1], [{}, [1]], [shared, [1, 2]]]),
+    ),
+    true,
+  );
+});
+
 test('util.isPartialDeepStrictEqual returns false with unexpected properties', () => {
   assert.strictEqual(
     util.isPartialDeepStrictEqual({ a: 1 }, { a: 2 }),