diff --git a/packages/pass-style/tools.js b/packages/pass-style/tools.js
index 78fd22bf37..50fd8ca393 100644
--- a/packages/pass-style/tools.js
+++ b/packages/pass-style/tools.js
@@ -10,6 +10,8 @@ export {
   exampleBob,
   exampleCarol,
   arbString,
+  arbKeyLeaf,
   arbLeaf,
+  arbKey,
   arbPassable,
 } from './tools/arb-passable.js';
diff --git a/packages/pass-style/tools/arb-passable.js b/packages/pass-style/tools/arb-passable.js
index 22549f5d83..5c6bcbdfbf 100644
--- a/packages/pass-style/tools/arb-passable.js
+++ b/packages/pass-style/tools/arb-passable.js
@@ -14,7 +14,7 @@ export const exampleCarol = Far('carol', {});
 
 export const arbString = fc.oneof(fc.string(), fc.fullUnicodeString());
 
-export const arbLeaf = fc.oneof(
+const keyableLeaves = [
   fc.constantFrom(null, undefined, false, true),
   arbString,
   arbString.map(s => Symbol.for(s)),
@@ -31,22 +31,43 @@ export const arbLeaf = fc.oneof(
   fc.constantFrom(-0, NaN, Infinity, -Infinity),
   fc.record({}),
   fc.constantFrom(exampleAlice, exampleBob, exampleCarol),
+];
+
+export const arbKeyLeaf = fc.oneof(...keyableLeaves);
+
+export const arbLeaf = fc.oneof(
+  ...keyableLeaves,
   arbString.map(s => Error(s)),
   // unresolved promise
   fc.constant(new Promise(() => {})),
 );
 
+const { keyDag } = fc.letrec(tie => {
+  return {
+    keyDag: fc.oneof(
+      { withCrossShrink: true },
+      arbKeyLeaf,
+      fc.array(tie('keyDag')),
+      fc.dictionary(
+        arbString.filter(s => s !== 'then'),
+        tie('keyDag'),
+      ),
+    ),
+  };
+});
+
 const { arbDag } = fc.letrec(tie => {
   return {
     arbDag: fc.oneof(
       { withCrossShrink: true },
       arbLeaf,
-      tie('arbDag').map(v => Promise.resolve(v)),
       fc.array(tie('arbDag')),
       fc.dictionary(
         arbString.filter(s => s !== 'then'),
         tie('arbDag'),
       ),
+      // A promise for a passable.
+      tie('arbDag').map(v => Promise.resolve(v)),
       // A tagged value, either of arbitrary type with arbitrary payload
       // or of known type with arbitrary or explicitly valid payload.
       // Ordered by increasing complexity.
@@ -110,6 +131,11 @@ const { arbDag } = fc.letrec(tie => {
 });
 
 /**
- * A factory for arbitrary passables
+ * A factory for arbitrary keys.
+ */
+export const arbKey = keyDag.map(x => harden(x));
+
+/**
+ * A factory for arbitrary passables.
  */
 export const arbPassable = arbDag.map(x => harden(x));
diff --git a/packages/patterns/package.json b/packages/patterns/package.json
index 701e5470e5..e1d806d0a8 100644
--- a/packages/patterns/package.json
+++ b/packages/patterns/package.json
@@ -40,7 +40,9 @@
   },
   "devDependencies": {
     "@endo/init": "workspace:^",
+    "@endo/pass-style": "workspace:^",
     "@endo/ses-ava": "workspace:^",
+    "@fast-check/ava": "^1.1.5",
     "ava": "^6.1.3",
     "babel-eslint": "^10.1.0",
     "eslint": "^8.57.0",
diff --git a/packages/patterns/test/copySet.test.js b/packages/patterns/test/copySet.test.js
index b46e79aa36..4912f9c1e1 100644
--- a/packages/patterns/test/copySet.test.js
+++ b/packages/patterns/test/copySet.test.js
@@ -1,12 +1,21 @@
 import test from '@endo/ses-ava/prepare-endo.js';
 
+import { fc } from '@fast-check/ava';
 import { makeTagged, getTag, passStyleOf } from '@endo/marshal';
+import {
+  arbKey,
+  exampleAlice,
+  exampleBob,
+  exampleCarol,
+} from '@endo/pass-style/tools.js';
+import { Fail, q } from '@endo/errors';
 import {
   isCopySet,
   assertCopySet,
   makeCopySet,
   getCopySetKeys,
 } from '../src/keys/checkKey.js';
+import { keyEQ } from '../src/keys/compareKeys.js';
 import {
   setIsSuperset,
   setIsDisjoint,
@@ -85,7 +94,7 @@ test('key uniqueness', t => {
 // TODO: incorporate fast-check for property-based testing that construction
 // reverse rank sorts keys and validation rejects any other key order.
 
-test('operations', t => {
+test('operations on golden inputs', t => {
   const x = makeCopySet(['b', 'a', 'c']);
   const y = makeCopySet(['a', 'b']);
   const z = makeCopySet(['c', 'b']);
@@ -104,6 +113,16 @@ test('operations', t => {
   t.assert(setIsDisjoint(xMy, y));
 
   t.assert(setIsSuperset(x, y));
+  const twoCohorts = [
+    [exampleAlice, 'z'],
+    [exampleBob, 'z'],
+    [exampleCarol, 'a'],
+  ];
+  t.assert(
+    setIsSuperset(makeCopySet(twoCohorts), makeCopySet(twoCohorts.slice(-1))),
+    'superset with many items in one rank cohort (issue #2588)',
+  );
+
   t.assert(matches(x, yUz));
   t.assert(matches(x, M.gt(y)));
   t.assert(matches(x, M.gt(z)));
@@ -119,6 +138,23 @@ test('operations', t => {
   t.deepEqual(yIz, makeTagged('copySet', ['b']));
 });
 
+test('setIsSuperset', async t => {
+  await fc.assert(
+    fc.property(
+      fc.uniqueArray(arbKey, { comparator: keyEQ }),
+      fc.infiniteStream(fc.boolean()),
+      (arr, keepSeq) => {
+        const sub = arr.filter(() => keepSeq.next().value);
+        setIsSuperset(makeCopySet(arr), makeCopySet(sub)) ||
+          Fail`${q(sub)} of ${q(arr)}`;
+      },
+    ),
+  );
+
+  // Ensure at least one ava assertion.
+  t.pass();
+});
+
 test('matching', t => {
   const copySet = makeCopySet(['z', 'c', 'b', 'a']);
   const missingKey = makeCopySet(['z', 'c', 'b']);
diff --git a/yarn.lock b/yarn.lock
index 27468a3e8a..6701d0ce66 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -727,8 +727,10 @@ __metadata:
     "@endo/eventual-send": "workspace:^"
     "@endo/init": "workspace:^"
     "@endo/marshal": "workspace:^"
+    "@endo/pass-style": "workspace:^"
     "@endo/promise-kit": "workspace:^"
     "@endo/ses-ava": "workspace:^"
+    "@fast-check/ava": "npm:^1.1.5"
     ava: "npm:^6.1.3"
     babel-eslint: "npm:^10.1.0"
     eslint: "npm:^8.57.0"