diff --git a/muted-tests.yml b/muted-tests.yml
index e63aa3e3746fe..41ec05258c865 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -93,6 +93,9 @@ tests:
 - class: org.elasticsearch.xpack.test.rest.XPackRestIT
   method: test {p0=transform/transforms_start_stop/Test start/stop only starts/stops specified transform}
   issue: https://github.com/elastic/elasticsearch/issues/126466
+- class: org.elasticsearch.repositories.blobstore.testkit.rest.SnapshotRepoTestKitClientYamlTestSuiteIT
+  method: test {p0=/10_analyze/Analysis without details}
+  issue: https://github.com/elastic/elasticsearch/issues/126569
 - class: org.elasticsearch.xpack.test.rest.XPackRestIT
   method: test {p0=transform/transforms_start_stop/Test start/stop/start continuous transform}
   issue: https://github.com/elastic/elasticsearch/issues/126755
@@ -264,9 +267,15 @@ tests:
 - class: org.elasticsearch.xpack.inference.action.filter.ShardBulkInferenceActionFilterBasicLicenseIT
   method: testLicenseInvalidForInference {p0=false}
   issue: https://github.com/elastic/elasticsearch/issues/137691
+- class: org.elasticsearch.xpack.inference.InferenceRestIT
+  method: test {p0=inference/70_text_similarity_rank_retriever/Text similarity reranker with min_score zero includes all docs}
+  issue: https://github.com/elastic/elasticsearch/issues/137732
 - class: org.elasticsearch.indices.mapping.UpdateMappingIntegrationIT
   method: testUpdateMappingConcurrently
   issue: https://github.com/elastic/elasticsearch/issues/137758
+- class: org.elasticsearch.xpack.inference.external.http.sender.RequestExecutorServiceTests
+  method: testChangingCapacity_DoesNotRejectsOverflowTasks_BecauseOfQueueFull
+  issue: https://github.com/elastic/elasticsearch/issues/137823
 - class: org.elasticsearch.xpack.inference.integration.AuthorizationTaskExecutorMultipleNodesIT
   method: testAuthorizationTaskGetsRelocatedToAnotherNode_WhenTheNodeThatIsRunningItShutsDown
   issue: https://github.com/elastic/elasticsearch/issues/137911
@@ -336,15 +345,9 @@ tests:
 - class: org.elasticsearch.smoketest.MlWithSecurityIT
   method: test {yaml=ml/sparse_vector_search/Test sparse_vector search with query vector and pruning config}
   issue: https://github.com/elastic/elasticsearch/issues/139196
-- class: org.elasticsearch.xpack.inference.integration.AuthorizationTaskExecutorIT
-  method: testCreatesEisChatCompletionEndpoint
-  issue: https://github.com/elastic/elasticsearch/issues/138764
 - class: org.elasticsearch.smoketest.SmokeTestMultiNodeClientYamlTestSuiteIT
   method: test {yaml=index/100_field_name_length_limit/Test field name length limit array synthetic source}
   issue: https://github.com/elastic/elasticsearch/issues/139300
-- class: org.elasticsearch.xpack.inference.integration.AuthorizationTaskExecutorIT
-  method: testCreatesChatCompletion_AndThenCreatesTextEmbedding
-  issue: https://github.com/elastic/elasticsearch/issues/138012
 - class: org.elasticsearch.xpack.unsignedlong.UnsignedLongSyntheticSourceNativeArrayIntegrationTests
   method: testSynthesizeArrayRandom
   issue: https://github.com/elastic/elasticsearch/issues/139376
diff --git a/x-pack/plugin/inference/src/internalClusterTest/java/org/elasticsearch/xpack/inference/integration/AuthorizationTaskExecutorIT.java b/x-pack/plugin/inference/src/internalClusterTest/java/org/elasticsearch/xpack/inference/integration/AuthorizationTaskExecutorIT.java
index 97d80174f5f59..acc478b16901d 100644
--- a/x-pack/plugin/inference/src/internalClusterTest/java/org/elasticsearch/xpack/inference/integration/AuthorizationTaskExecutorIT.java
+++ b/x-pack/plugin/inference/src/internalClusterTest/java/org/elasticsearch/xpack/inference/integration/AuthorizationTaskExecutorIT.java
@@ -75,12 +75,13 @@ public class AuthorizationTaskExecutorIT extends ESSingleNodeTestCase {
     public static void initClass() throws IOException {
         webServer.start();
         gatewayUrl = getUrl(webServer);
-        webServer.enqueue(new MockResponse().setResponseCode(200).setBody(EIS_EMPTY_RESPONSE));
         chatCompletionResponseBody = getEisRainbowSprinklesAuthorizationResponse(gatewayUrl).responseJson();
     }
 
     @Before
     public void createComponents() {
+        // Adding an empty response to ensure that the initial authorization polling request does not fail
+        webServer.enqueue(new MockResponse().setResponseCode(200).setBody(EIS_EMPTY_RESPONSE));
         modelRegistry = node().injector().getInstance(ModelRegistry.class);
         authorizationTaskExecutor = node().injector().getInstance(AuthorizationTaskExecutor.class);
     }
@@ -195,7 +196,7 @@ private List<UnparsedModel> getEisEndpoints() {
 
     static List<UnparsedModel> getEisEndpoints(ModelRegistry modelRegistry) {
         var listener = new PlainActionFuture<List<UnparsedModel>>();
-        modelRegistry.getAllModels(false, listener);
+        modelRegistry.getAllModels(true, listener);
 
         var endpoints = listener.actionGet(TimeValue.THIRTY_SECONDS);
         return endpoints.stream().filter(m -> m.service().equals(ElasticInferenceService.NAME)).toList();