diff --git a/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.toml b/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.toml
index c36db8b41126..c050726217b9 100644
--- a/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.toml
+++ b/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.toml
@@ -1,13 +1,16 @@
 [settings]
 timeout = 1000
 
-[relaychain]
-default_image = "{{ZOMBIENET_INTEGRATION_TEST_IMAGE}}"
-chain = "rococo-local"
+[relaychain.genesis.runtimeGenesis.patch.configuration.config.async_backing_params]
+max_candidate_depth = 6
 
 [relaychain.genesis.runtimeGenesis.patch.configuration.config.scheduler_params]
 num_cores = 2
 
+[relaychain]
+default_image = "{{ZOMBIENET_INTEGRATION_TEST_IMAGE}}"
+chain = "rococo-local"
+
 [relaychain.default_resources]
 limits = { memory = "4G", cpu = "2" }
 requests = { memory = "2G", cpu = "1" }
@@ -18,11 +21,15 @@ requests = { memory = "2G", cpu = "1" }
 
   [[relaychain.nodes]]
   name = "bob"
-  args = [ "--bob", "-lparachain=debug,runtime=debug"]
+  args = [ "--bob", "-lparachain=debug,runtime=debug" ]
 
   [[relaychain.nodes]]
   name = "charlie"
   args = [ "--charlie", "-lparachain=debug,runtime=debug" ]
+  
+  [[relaychain.nodes]]
+  name = "dave"
+  args = [ "--dave", "-lparachain=debug,runtime=debug" ]
 
 [[parachains]]
 id = 2000
diff --git a/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.zndsl b/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.zndsl
index 460be92c04a4..cefe1ec2d4ad 100644
--- a/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.zndsl
+++ b/polkadot/zombienet_tests/functional/0020-same-collation-to-all-assigned-cores.zndsl
@@ -6,12 +6,15 @@ Creds: config
 alice: reports node_roles is 4
 bob: reports node_roles is 4
 charlie: reports node_roles is 4
+dave: reports node_roles is 4
 
 # Ensure parachains are registered.
 alice: parachain 2000 is registered within 60 seconds
 
-# Register the second core assigned to this parachain.
+# Register three cores assigned to this parachain.
 alice: js-script ./assign-core.js with "0,2000,57600" return is 0 within 600 seconds
+bob: js-script ./assign-core.js with "1,2000,57600" return is 0 within 600 seconds
+charlie: js-script ./assign-core.js with "2,2000,57600" return is 0 within 600 seconds
 
 # Ensure parachains made progress.
 alice: parachain 2000 block height is at least 10 within 300 seconds