diff --git a/.github/workflows/test_onnxruntime.yml b/.github/workflows/test_onnxruntime.yml
index 089300f7cd9..fec5c7e5b27 100644
--- a/.github/workflows/test_onnxruntime.yml
+++ b/.github/workflows/test_onnxruntime.yml
@@ -18,8 +18,10 @@ jobs:
       fail-fast: false
       matrix:
         transformers-version: ["latest"]
-        os: [ubuntu-20.04, windows-2019, macos-13]
+        os: [ubuntu-20.04, windows-2019, macos-15]
         include:
+          - transformers-version: "4.36.*"
+            os: ubuntu-20.04
           - transformers-version: "4.45.*"
             os: ubuntu-20.04
 
diff --git a/optimum/exporters/onnx/model_configs.py b/optimum/exporters/onnx/model_configs.py
index cc752779d30..6b92109b7b6 100644
--- a/optimum/exporters/onnx/model_configs.py
+++ b/optimum/exporters/onnx/model_configs.py
@@ -295,7 +295,7 @@ class Qwen2OnnxConfig(LlamaOnnxConfig):
 class GemmaOnnxConfig(LlamaOnnxConfig):
     DUMMY_INPUT_GENERATOR_CLASSES = (DummyTextInputGenerator, GemmaDummyPastKeyValuesGenerator)
     DUMMY_PKV_GENERATOR_CLASS = GemmaDummyPastKeyValuesGenerator
-    pass
+    MIN_TRANSFORMERS_VERSION = version.parse("4.38.0")
 
 
 class GraniteOnnxConfig(LlamaOnnxConfig):
@@ -348,6 +348,8 @@ def patch_model_for_export(
 class MPTOnnxConfig(TextDecoderOnnxConfig):
     # MPT does not require position_ids input.
     DEFAULT_ONNX_OPSET = 13
+    # TODO: fix inference for transformers < v4.41 for beam_search > 1
+    MIN_TRANSFORMERS_VERSION = version.parse("4.41.0")
     NORMALIZED_CONFIG_CLASS = NormalizedTextConfig.with_args(
         num_attention_heads="n_heads", hidden_size="d_model", num_layers="n_layers"
     )
diff --git a/setup.py b/setup.py
index 7ea0da56c29..29f97b604e0 100644
--- a/setup.py
+++ b/setup.py
@@ -54,7 +54,7 @@
         "datasets>=1.2.1",
         "evaluate",
         "protobuf>=3.20.1",
-        "transformers<4.47.0",
+        "transformers>=4.36,<4.47.0",
     ],
     "onnxruntime-gpu": [
         "onnx",
@@ -63,19 +63,19 @@
         "evaluate",
         "protobuf>=3.20.1",
         "accelerate",  # ORTTrainer requires it.
-        "transformers<4.47.0",
+        "transformers>=4.36,<4.47.0",
     ],
     "exporters": [
         "onnx",
         "onnxruntime",
         "timm",
-        "transformers<4.47.0",
+        "transformers>=4.36,<4.47.0",
     ],
     "exporters-gpu": [
         "onnx",
         "onnxruntime-gpu",
         "timm",
-        "transformers<4.47.0",
+        "transformers>=4.36,<4.47.0",
     ],
     "exporters-tf": [
         "tensorflow>=2.4,<=2.12.1",
@@ -86,7 +86,7 @@
         "h5py",
         "numpy<1.24.0",
         "datasets<=2.16",
-        "transformers>=4.26,<4.38",
+        "transformers>=4.36,<4.38",
     ],
     "diffusers": ["diffusers"],
     "intel": "optimum-intel>=1.18.0",
diff --git a/tests/onnxruntime/test_modeling.py b/tests/onnxruntime/test_modeling.py
index a335e014478..84ac27029f9 100644
--- a/tests/onnxruntime/test_modeling.py
+++ b/tests/onnxruntime/test_modeling.py
@@ -2318,21 +2318,28 @@ class ORTModelForCausalLMIntegrationTest(ORTModelTestMixin):
         "bloom",
         "codegen",
         "falcon",
-        "gemma",
         "gpt2",
         "gpt_bigcode",
         "gpt_neo",
         "gpt_neox",
         "gptj",
-        "granite",
         "llama",
         "mistral",
-        "mpt",
         "opt",
     ]
 
-    if check_if_transformers_greater("4.40"):
-        SUPPORTED_ARCHITECTURES.extend(["gemma", "phi3", "qwen2"])
+    if check_if_transformers_greater("4.37"):
+        SUPPORTED_ARCHITECTURES.append("qwen2")
+
+    if check_if_transformers_greater("4.38"):
+        SUPPORTED_ARCHITECTURES.append("gemma")
+
+    # TODO: fix "mpt" for which inference fails for transformers < v4.41
+    if check_if_transformers_greater("4.41"):
+        SUPPORTED_ARCHITECTURES.extend(["phi3", "mpt"])
+
+    if check_if_transformers_greater("4.45"):
+        SUPPORTED_ARCHITECTURES.append("granite")
 
     FULL_GRID = {
         "model_arch": SUPPORTED_ARCHITECTURES,
@@ -2445,7 +2452,7 @@ def test_compare_to_transformers(self, test_name: str, model_arch: str, use_cach
         transformers_model = AutoModelForCausalLM.from_pretrained(model_id)
         transformers_model = transformers_model.eval()
         tokenizer = get_preprocessor(model_id)
-        tokens = tokenizer("This is a sample output", return_tensors="pt")
+        tokens = tokenizer("This is a sample input", return_tensors="pt")
         position_ids = None
         if model_arch.replace("_", "-") in MODEL_TYPES_REQUIRING_POSITION_IDS:
             input_shape = tokens["input_ids"].shape
@@ -2467,7 +2474,7 @@ def test_compare_to_transformers(self, test_name: str, model_arch: str, use_cach
         # Compare batched generation.
         tokenizer.pad_token_id = tokenizer.eos_token_id
         tokenizer.padding_side = "left"
-        tokens = tokenizer(["Today is a nice day and I am longer", "This is me"], return_tensors="pt", padding=True)
+        tokens = tokenizer(["This is", "This is a sample input"], return_tensors="pt", padding=True)
         onnx_model.generation_config.eos_token_id = None
         transformers_model.generation_config.eos_token_id = None
         onnx_model.config.eos_token_id = None
@@ -4598,14 +4605,14 @@ def test_compare_with_and_without_past_key_values(self, model_arch: str):
             )
 
         self.assertTrue(torch.equal(outputs_model_with_pkv, outputs_model_without_pkv))
-        self.assertEqual(
-            outputs_model_with_pkv.shape[1],
-            self.GENERATION_LENGTH + 2 if model_arch == "whisper" else self.GENERATION_LENGTH + 1,
-        )
-        self.assertEqual(
-            outputs_model_without_pkv.shape[1],
-            self.GENERATION_LENGTH + 2 if model_arch == "whisper" else self.GENERATION_LENGTH + 1,
-        )
+
+        if model_arch == "whisper" and check_if_transformers_greater("4.43"):
+            gen_length = self.GENERATION_LENGTH + 2
+        else:
+            gen_length = self.GENERATION_LENGTH + 1
+
+        self.assertEqual(outputs_model_with_pkv.shape[1], gen_length)
+        self.assertEqual(outputs_model_without_pkv.shape[1], gen_length)
 
         self.GENERATION_LENGTH = generation_length
         if os.environ.get("TEST_LEVEL", 0) == "1":