diff --git a/packages/credential-sdk/src/modules/tests/offchain-signatures-module.js b/packages/credential-sdk/src/modules/tests/offchain-signatures-module.js
index 3ce29cda6..cb77a82c6 100644
--- a/packages/credential-sdk/src/modules/tests/offchain-signatures-module.js
+++ b/packages/credential-sdk/src/modules/tests/offchain-signatures-module.js
@@ -29,7 +29,7 @@ export default function generateOffchainSignatureModuleTests(
 ) {
   const test = itIf(filter);
 
-  describe(`Using ${didModule.constructor.name} and ${offchainSignatures.constructor.name}`, () => {
+  describe(`Checks ${didModule.constructor.name} and ${offchainSignatures.constructor.name} with all public keys and params`, () => {
     test('Generates a `DIDDocument` with `OffchainPublicKey` and creates a `OffchainParameters` owned by this DID', async () => {
       const did = DID.random();
 
@@ -129,15 +129,54 @@ export default function generateOffchainSignatureModuleTests(
       });
     });
 
-    const modules = [bbs, bbsPlus, ps];
-    const keysClasses = [BBSPublicKey, BBSPlusPublicKey, PSPublicKey];
-    const paramsClasses = [BBSParams, BBSPlusParams, PSParams];
-    for (let idx = 0; idx < keysClasses.length; idx++) {
-      const module = modules[idx];
-      const PublicKey = keysClasses[idx];
-      const Params = paramsClasses[idx];
+    test('Returns `null` in case of missing params', async () => {
+      const did = DID.random();
+      const keyPair = Ed25519Keypair.random();
+      const didKeypair = new DidKeypair([did, 1], keyPair);
+
+      const document = DIDDocument.create(did, [didKeypair.didKey()]);
+
+      const psParamsId = await offchainSignatures.nextParamsId(did);
+      const psParamsRef = new OffchainSignaturesParamsRef(did, psParamsId);
+
+      await didModule.createDocument(document, didKeypair);
+      const psKey = new PSPublicKey(
+        new PSPublicKeyValue(TypedBytes.random(1000), psParamsRef),
+      );
 
-      test(`Checks ${module.constructor.name}`, async () => {
+      expect(
+        await offchainSignatures.getParams(
+          did,
+          await offchainSignatures.nextParamsId(did),
+        ),
+      ).toBe(null);
+
+      await expect(() => psKey.withParams(offchainSignatures)).rejects.toThrow();
+    });
+  });
+
+  const cases = [
+    {
+      module: bbs,
+      PublicKey: BBSPublicKey,
+      Params: BBSParams,
+    },
+    {
+      module: bbsPlus,
+      PublicKey: BBSPlusPublicKey,
+      Params: BBSPlusParams,
+    },
+    {
+      module: ps,
+      PublicKey: PSPublicKey,
+      Params: PSParams,
+    },
+  ];
+
+  describe.each(cases)(
+    'Checks basic workflow for each module',
+    ({ module, PublicKey, Params }) => {
+      test(`Generates a \`DIDDocument\` with \`OffchainPublicKey\` and creates a \`OffchainParameters\` owned by this DID using ${module.constructor.name} with ${PublicKey.name} and ${Params.name}`, async () => {
         const did = DID.random();
 
         const keyPair = Ed25519Keypair.random();
@@ -156,6 +195,9 @@ export default function generateOffchainSignatureModuleTests(
             stringToU8a(module.constructor.name),
           ),
         );
+
+        expect(await module.getParams(did, id)).toEqual(null);
+
         await module.addParams(id, params, did, didKeypair);
 
         const key = new PublicKey(
@@ -177,31 +219,6 @@ export default function generateOffchainSignatureModuleTests(
           params.toJSON(),
         );
       });
-    }
-
-    test('Returns `null` in case of missing params', async () => {
-      const did = DID.random();
-      const keyPair = Ed25519Keypair.random();
-      const didKeypair = new DidKeypair([did, 1], keyPair);
-
-      const document = DIDDocument.create(did, [didKeypair.didKey()]);
-
-      const psParamsId = await offchainSignatures.nextParamsId(did);
-      const psParamsRef = new OffchainSignaturesParamsRef(did, psParamsId);
-
-      await didModule.createDocument(document, didKeypair);
-      const psKey = new PSPublicKey(
-        new PSPublicKeyValue(TypedBytes.random(1000), psParamsRef),
-      );
-
-      expect(
-        await offchainSignatures.getParams(
-          did,
-          await offchainSignatures.nextParamsId(did),
-        ),
-      ).toBe(null);
-
-      await expect(() => psKey.withParams(offchainSignatures)).rejects.toThrow();
-    });
-  });
+    },
+  );
 }
diff --git a/packages/dock-blockchain-modules/tests/integration/modules/offchain-signatures-module.test.js b/packages/dock-blockchain-modules/tests/integration/modules/offchain-signatures-module.test.js
index e2ed88cae..56b5dc419 100644
--- a/packages/dock-blockchain-modules/tests/integration/modules/offchain-signatures-module.test.js
+++ b/packages/dock-blockchain-modules/tests/integration/modules/offchain-signatures-module.test.js
@@ -4,7 +4,13 @@ import {
   MultiApiOffchainSignaturesModule,
   MultiApiDIDModule,
 } from "@docknetwork/credential-sdk/modules";
-import { DockDIDModule, DockOffchainSignaturesModule } from "../../../src";
+import {
+  DockDIDModule,
+  DockOffchainSignaturesModule,
+  DockBBSModule,
+  DockBBSPlusModule,
+  DockPSModule,
+} from "../../../src";
 import {
   FullNodeEndpoint,
   TestAccountURI,
@@ -35,6 +41,9 @@ describe("BlobModule", () => {
     {
       did: new DockDIDModule(dock),
       offchainSignatures: new DockOffchainSignaturesModule(dock),
+      bbs: new DockBBSModule(dock),
+      bbsPlus: new DockBBSPlusModule(dock),
+      ps: new DockPSModule(dock),
     },
     {
       DID: DockDid,
@@ -48,6 +57,11 @@ describe("BlobModule", () => {
       offchainSignatures: new MultiApiOffchainSignaturesModule([
         new DockOffchainSignaturesModule(dock),
       ]),
+      bbs: new MultiApiOffchainSignaturesModule([new DockBBSModule(dock)]),
+      bbsPlus: new MultiApiOffchainSignaturesModule([
+        new DockBBSPlusModule(dock),
+      ]),
+      ps: new MultiApiOffchainSignaturesModule([new DockPSModule(dock)]),
     },
     {
       DID: DockDid,