diff --git a/agent/auxiliary_client.py b/agent/auxiliary_client.py
index 8ea986f816..1e1931d0d6 100644
--- a/agent/auxiliary_client.py
+++ b/agent/auxiliary_client.py
@@ -1349,21 +1349,27 @@ def _is_auth_error(exc: Exception) -> bool:
     return "error code: 401" in err_lower or "authenticationerror" in type(exc).__name__.lower()
 
 
-def _is_unsupported_temperature_error(exc: Exception) -> bool:
-    """Detect API errors where the selected model rejects `temperature`.
+def _is_unsupported_parameter_error(exc: Exception, param: str) -> bool:
+    """Detect provider 400s for an unsupported request parameter.
 
-    Triggered by provider responses like:
-      * OpenAI / Codex Responses — ``Unsupported parameter: temperature``
-      * Copilot reasoning models — ``unsupported_parameter`` with temperature
-      * OpenRouter reasoning models — ``does not support temperature``
-      * Anthropic Opus 4.7+ via OpenAI-compat — ``temperature is not supported``
+    Different OpenAI-compatible endpoints phrase the same class of error a few
+    ways: ``Unsupported parameter: X``, ``unsupported_parameter`` with a
+    ``param`` field, ``X is not supported``, ``unknown parameter: X``,
+    ``unrecognized request argument: X``.  We match on both the parameter
+    name and a generic "unsupported/unknown/unrecognized parameter" marker so
+    call sites can reactively retry without the offending key instead of
+    surfacing a noisy auxiliary failure.
 
-    The same backend can accept temperature for some models and reject it for
-    others (e.g. gpt-5.4 accepts, gpt-5.5 rejects on the same endpoint), so we
-    react to the concrete error rather than maintaining a model allowlist.
+    Generalizes the temperature-specific detector that originally shipped
+    with PR #15621 so the same retry strategy can cover ``max_tokens``,
+    ``seed``, ``top_p``, and any future quirk. Credit @nicholasrae (PR #15416)
+    for the generalization pattern.
     """
+    param_lower = (param or "").lower()
+    if not param_lower:
+        return False
     err_lower = str(exc).lower()
-    if "temperature" not in err_lower:
+    if param_lower not in err_lower:
         return False
     return any(marker in err_lower for marker in (
         "unsupported parameter",
@@ -1372,9 +1378,20 @@ def _is_unsupported_temperature_error(exc: Exception) -> bool:
         "does not support",
         "unknown parameter",
         "unrecognized request argument",
+        "unrecognized parameter",
+        "invalid parameter",
     ))
 
 
+def _is_unsupported_temperature_error(exc: Exception) -> bool:
+    """Back-compat wrapper: detect API errors where the model rejects ``temperature``.
+
+    Delegates to :func:`_is_unsupported_parameter_error`; kept as a separate
+    public symbol because existing tests and call sites import it by name.
+    """
+    return _is_unsupported_parameter_error(exc, "temperature")
+
+
 def _evict_cached_clients(provider: str) -> None:
     """Drop cached auxiliary clients for a provider so fresh creds are used."""
     normalized = _normalize_aux_provider(provider)
@@ -3012,7 +3029,11 @@ def call_llm(
                 kwargs = retry_kwargs
 
         err_str = str(first_err)
-        if "max_tokens" in err_str or "unsupported_parameter" in err_str:
+        if max_tokens is not None and (
+            "max_tokens" in err_str
+            or "unsupported_parameter" in err_str
+            or _is_unsupported_parameter_error(first_err, "max_tokens")
+        ):
             kwargs.pop("max_tokens", None)
             kwargs["max_completion_tokens"] = max_tokens
             try:
@@ -3299,7 +3320,11 @@ async def async_call_llm(
                 kwargs = retry_kwargs
 
         err_str = str(first_err)
-        if "max_tokens" in err_str or "unsupported_parameter" in err_str:
+        if max_tokens is not None and (
+            "max_tokens" in err_str
+            or "unsupported_parameter" in err_str
+            or _is_unsupported_parameter_error(first_err, "max_tokens")
+        ):
             kwargs.pop("max_tokens", None)
             kwargs["max_completion_tokens"] = max_tokens
             try:
diff --git a/tests/agent/test_unsupported_parameter_retry.py b/tests/agent/test_unsupported_parameter_retry.py
new file mode 100644
index 0000000000..99745dc120
--- /dev/null
+++ b/tests/agent/test_unsupported_parameter_retry.py
@@ -0,0 +1,201 @@
+"""Regression tests for the generic unsupported-parameter detector in
+``agent.auxiliary_client``.
+
+The original temperature-specific detector (PR #15621) was generalized so the
+same reactive-retry strategy covers any provider that rejects an arbitrary
+request parameter — ``max_tokens``, ``seed``, ``top_p``, future quirks — not
+just ``temperature``. Credit @nicholasrae (PR #15416) for the generalization
+pattern.
+
+These tests lock in:
+  * ``_is_unsupported_parameter_error(exc, param)`` across common phrasings
+  * the back-compat wrapper ``_is_unsupported_temperature_error`` still works
+  * the max_tokens retry branch no longer pops a key that was never set
+    (``max_tokens is None`` gate)
+  * the max_tokens retry branch matches via the generic helper on top of the
+    legacy ``"max_tokens"`` / ``"unsupported_parameter"`` substring checks
+"""
+
+from unittest.mock import patch, MagicMock, AsyncMock
+
+import pytest
+
+from agent.auxiliary_client import (
+    call_llm,
+    async_call_llm,
+    _is_unsupported_parameter_error,
+    _is_unsupported_temperature_error,
+)
+
+
+class TestIsUnsupportedParameterError:
+    """The generic detector must match real provider phrasings for any param."""
+
+    @pytest.mark.parametrize("param,message", [
+        # temperature phrasings (regression coverage via the generic API)
+        ("temperature", "HTTP 400: Unsupported parameter: temperature"),
+        ("temperature", "Error code: 400 - {'error': {'code': 'unsupported_parameter', 'param': 'temperature'}}"),
+        ("temperature", "this model does not support temperature"),
+        # max_tokens phrasings
+        ("max_tokens", "HTTP 400: Unsupported parameter: max_tokens"),
+        ("max_tokens", "Unknown parameter: max_tokens — use max_completion_tokens"),
+        ("max_tokens", "Invalid parameter: max_tokens is not supported"),
+        # arbitrary future params
+        ("seed", "HTTP 400: unrecognized parameter: seed"),
+        ("top_p", "Error: top_p is not supported for this model"),
+    ])
+    def test_matches_real_provider_messages(self, param, message):
+        assert _is_unsupported_parameter_error(RuntimeError(message), param) is True
+
+    @pytest.mark.parametrize("param,message", [
+        # Param not mentioned at all
+        ("temperature", "HTTP 400: max_tokens is too large"),
+        # Param mentioned but not flagged as unsupported
+        ("temperature", "temperature must be between 0 and 2"),
+        # Totally unrelated 400
+        ("max_tokens", "Rate limit exceeded"),
+        # Connection-level errors
+        ("temperature", "Connection reset by peer"),
+    ])
+    def test_does_not_match_unrelated_errors(self, param, message):
+        assert _is_unsupported_parameter_error(RuntimeError(message), param) is False
+
+    def test_empty_param_returns_false(self):
+        assert _is_unsupported_parameter_error(
+            RuntimeError("HTTP 400: Unsupported parameter: temperature"), ""
+        ) is False
+
+    def test_temperature_wrapper_delegates_to_generic(self):
+        """Back-compat: ``_is_unsupported_temperature_error`` still routes through."""
+        msg = "HTTP 400: Unsupported parameter: temperature"
+        assert _is_unsupported_temperature_error(RuntimeError(msg)) is True
+        # And the unrelated-case still holds
+        assert _is_unsupported_temperature_error(
+            RuntimeError("max_tokens is too large")) is False
+
+
+def _dummy_response():
+    """Sentinel — real code calls ``_validate_llm_response`` which we patch out."""
+    return {"ok": True}
+
+
+class TestMaxTokensRetryHardening:
+    """The max_tokens retry branch now (a) gates on ``max_tokens is not None``
+    and (b) also matches the generic phrasings via the helper.
+    """
+
+    def test_sync_max_tokens_retry_skipped_when_max_tokens_is_none(self):
+        """No max_tokens kwarg → must not pop/retry even if the error mentions it.
+
+        Before the hardening, ``kwargs.pop("max_tokens", None)`` was safe but
+        ``kwargs["max_completion_tokens"] = max_tokens`` would set a None
+        value and hit the provider again. The gate skips the whole branch.
+        """
+        client = MagicMock()
+        client.base_url = "https://api.openai.com/v1"
+        err = RuntimeError("HTTP 400: Unsupported parameter: max_tokens")
+        client.chat.completions.create.side_effect = err
+
+        with (
+            patch("agent.auxiliary_client._resolve_task_provider_model",
+                  return_value=("openai-codex", "gpt-5.5", None, None, None)),
+            patch("agent.auxiliary_client._get_cached_client",
+                  return_value=(client, "gpt-5.5")),
+            patch("agent.auxiliary_client._validate_llm_response",
+                  side_effect=lambda resp, _task: resp),
+        ):
+            with pytest.raises(RuntimeError):
+                call_llm(
+                    task="session_search",
+                    messages=[{"role": "user", "content": "hi"}],
+                    temperature=0.3,
+                    # max_tokens omitted on purpose
+                )
+
+        # Only the initial attempt — no retry because the gate blocked it
+        assert client.chat.completions.create.call_count == 1
+
+    def test_sync_max_tokens_retry_matches_generic_phrasing(self):
+        """A 400 saying "Unknown parameter: max_tokens" (not the legacy
+        substring ``"max_tokens"`` bare + no ``unsupported_parameter`` token)
+        now triggers the retry via the generic helper.
+        """
+        client = MagicMock()
+        client.base_url = "https://api.openai.com/v1"
+        err = RuntimeError("Unknown parameter: max_tokens")
+        response = _dummy_response()
+        client.chat.completions.create.side_effect = [err, response]
+
+        with (
+            patch("agent.auxiliary_client._resolve_task_provider_model",
+                  return_value=("openai-codex", "gpt-5.5", None, None, None)),
+            patch("agent.auxiliary_client._get_cached_client",
+                  return_value=(client, "gpt-5.5")),
+            patch("agent.auxiliary_client._validate_llm_response",
+                  side_effect=lambda resp, _task: resp),
+        ):
+            result = call_llm(
+                task="session_search",
+                messages=[{"role": "user", "content": "hi"}],
+                temperature=0.3,
+                max_tokens=512,
+            )
+
+        assert result is response
+        assert client.chat.completions.create.call_count == 2
+        second_call = client.chat.completions.create.call_args_list[1]
+        assert "max_tokens" not in second_call.kwargs
+        assert second_call.kwargs["max_completion_tokens"] == 512
+
+    @pytest.mark.asyncio
+    async def test_async_max_tokens_retry_skipped_when_max_tokens_is_none(self):
+        client = MagicMock()
+        client.base_url = "https://api.openai.com/v1"
+        err = RuntimeError("HTTP 400: Unsupported parameter: max_tokens")
+        client.chat.completions.create = AsyncMock(side_effect=err)
+
+        with (
+            patch("agent.auxiliary_client._resolve_task_provider_model",
+                  return_value=("openai-codex", "gpt-5.5", None, None, None)),
+            patch("agent.auxiliary_client._get_cached_client",
+                  return_value=(client, "gpt-5.5")),
+            patch("agent.auxiliary_client._validate_llm_response",
+                  side_effect=lambda resp, _task: resp),
+        ):
+            with pytest.raises(RuntimeError):
+                await async_call_llm(
+                    task="session_search",
+                    messages=[{"role": "user", "content": "hi"}],
+                    temperature=0.3,
+                )
+
+        assert client.chat.completions.create.call_count == 1
+
+    @pytest.mark.asyncio
+    async def test_async_max_tokens_retry_matches_generic_phrasing(self):
+        client = MagicMock()
+        client.base_url = "https://api.openai.com/v1"
+        err = RuntimeError("Unknown parameter: max_tokens")
+        response = _dummy_response()
+        client.chat.completions.create = AsyncMock(side_effect=[err, response])
+
+        with (
+            patch("agent.auxiliary_client._resolve_task_provider_model",
+                  return_value=("openai-codex", "gpt-5.5", None, None, None)),
+            patch("agent.auxiliary_client._get_cached_client",
+                  return_value=(client, "gpt-5.5")),
+            patch("agent.auxiliary_client._validate_llm_response",
+                  side_effect=lambda resp, _task: resp),
+        ):
+            result = await async_call_llm(
+                task="session_search",
+                messages=[{"role": "user", "content": "hi"}],
+                temperature=0.3,
+                max_tokens=512,
+            )
+
+        assert result is response
+        assert client.chat.completions.create.await_count == 2
+        second_call = client.chat.completions.create.call_args_list[1]
+        assert "max_tokens" not in second_call.kwargs
+        assert second_call.kwargs["max_completion_tokens"] == 512