diff --git a/README.md b/README.md
index 1018b08..a7218ad 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,10 @@
 
 Pytest plugin for automatically mocking OpenAI requests. Powered by [RESPX](https://github.com/lundberg/respx).
 
-[![sdk support](https://img.shields.io/badge/SDK_Support-v1.25+-white?logo=openai&logoColor=black&labelColor=white)](https://github.com/openai/openai-python)
+[![sdk support](https://img.shields.io/badge/SDK_Support-v1.32+-white?logo=openai&logoColor=black&labelColor=white)](https://github.com/openai/openai-python)
+
+> [!NOTE]
+> For working with OpenAI Python SDK versions `>=1.25,<1.32` please use version `0.6` or earlier for this library
 
 ## Supported Endpoints
 
diff --git a/pyproject.toml b/pyproject.toml
index 5ecd67d..6180a2a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -22,7 +22,7 @@ openai_responses = "openai_responses.plugin"
 python = ">=3.9,<4.0"
 faker = ">=24.2.0,<25.0.0"
 faker-openai-api-provider = "0.2.0"
-openai = ">=1.25,<1.32"
+openai = ">=1.32,<1.35"
 requests-toolbelt = "^1.0.0"
 respx = "^0.20.2"
 
diff --git a/src/openai_responses/_routes/runs.py b/src/openai_responses/_routes/runs.py
index 4a879fb..9bf95e6 100644
--- a/src/openai_responses/_routes/runs.py
+++ b/src/openai_responses/_routes/runs.py
@@ -90,6 +90,7 @@ def _build(partial: PartialRun, request: httpx.Request) -> Run:
             "created_at": utcnow_unix_timestamp_s(),
             "instructions": "",
             "object": "thread.run",
+            "parallel_tool_calls": True,
             "status": "queued",
         }
         return model_parse(Run, defaults | partial | content)
diff --git a/src/openai_responses/_types/partials/runs.py b/src/openai_responses/_types/partials/runs.py
index 2709195..2af6d26 100644
--- a/src/openai_responses/_types/partials/runs.py
+++ b/src/openai_responses/_types/partials/runs.py
@@ -94,6 +94,7 @@ class PartialRun(TypedDict):
     metadata: NotRequired[Dict[str, str]]
     model: NotRequired[str]
     object: NotRequired[Literal["thread.run"]]
+    parallel_tool_calls: NotRequired[bool]
     required_action: NotRequired[PartialRequiredAction]
     response_format: NotRequired[
         Union[Literal["none", "auto"], PartialAssistantResponseFormat]
diff --git a/tests/unit/test_state_store.py b/tests/unit/test_state_store.py
index ca94b27..4ee1a77 100644
--- a/tests/unit/test_state_store.py
+++ b/tests/unit/test_state_store.py
@@ -169,6 +169,7 @@ def test_run_store(state_store: StateStore):
         instructions="",
         model="",
         object="thread.run",
+        parallel_tool_calls=True,
         status="in_progress",
         thread_id="thread_abc123",
         tools=[],
@@ -193,6 +194,7 @@ def test_run_store(state_store: StateStore):
                 instructions="",
                 model="",
                 object="thread.run",
+                parallel_tool_calls=True,
                 status="in_progress",
                 thread_id="thread_abc123",
                 tools=[],