diff --git a/src/poetry/puzzle/provider.py b/src/poetry/puzzle/provider.py
index cfcbc6048e8..d55bd1d0499 100644
--- a/src/poetry/puzzle/provider.py
+++ b/src/poetry/puzzle/provider.py
@@ -125,7 +125,7 @@ def __init__(
         self._direct_origin = DirectOrigin(self._pool.artifact_cache)
         self._io = io
         self._env: Env | None = None
-        self._python_constraint = package.python_constraint
+        self._package_python_constraint = package.python_constraint
         self._is_debugging: bool = self._io.is_debug() or self._io.is_very_verbose()
         self._overrides: dict[Package, dict[str, Dependency]] = {}
         self._deferred_cache: dict[Dependency, Package] = {}
@@ -159,11 +159,29 @@ def pool(self) -> RepositoryPool:
     def use_latest(self) -> Collection[NormalizedName]:
         return self._use_latest
 
+    @functools.cached_property
+    def _overrides_marker_intersection(self) -> BaseMarker:
+        overrides_marker_intersection: BaseMarker = AnyMarker()
+        for dep_overrides in self._overrides.values():
+            for dep in dep_overrides.values():
+                overrides_marker_intersection = overrides_marker_intersection.intersect(
+                    dep.marker
+                )
+        return overrides_marker_intersection
+
+    @functools.cached_property
+    def _python_constraint(self) -> VersionConstraint:
+        return self._package_python_constraint.intersect(
+            get_python_constraint_from_marker(self._overrides_marker_intersection)
+        )
+
     def is_debugging(self) -> bool:
         return self._is_debugging
 
     def set_overrides(self, overrides: dict[Package, dict[str, Dependency]]) -> None:
         self._overrides = overrides
+        self.__dict__.pop("_python_constraint", None)
+        self.__dict__.pop("_overrides_marker_intersection", None)
 
     def load_deferred(self, load_deferred: bool) -> None:
         self._load_deferred = load_deferred
@@ -180,16 +198,18 @@ def use_source_root(self, source_root: Path) -> Iterator[Provider]:
 
     @contextmanager
     def use_environment(self, env: Env) -> Iterator[Provider]:
-        original_python_constraint = self._python_constraint
+        original_python_constraint = self._package_python_constraint
 
         self._env = env
-        self._python_constraint = Version.parse(env.marker_env["python_full_version"])
+        self._package_python_constraint = Version.parse(
+            env.marker_env["python_full_version"]
+        )
 
         try:
             yield self
         finally:
             self._env = None
-            self._python_constraint = original_python_constraint
+            self._package_python_constraint = original_python_constraint
 
     @contextmanager
     def use_latest_for(self, names: Collection[NormalizedName]) -> Iterator[Provider]:
@@ -627,16 +647,12 @@ def complete_package(
                 continue
 
             # Sort out irrelevant requirements
-            overrides_marker_intersection: BaseMarker = AnyMarker()
-            for dep_overrides in self._overrides.values():
-                for dep in dep_overrides.values():
-                    overrides_marker_intersection = (
-                        overrides_marker_intersection.intersect(dep.marker)
-                    )
             deps = [
                 dep
                 for dep in deps
-                if not overrides_marker_intersection.intersect(dep.marker).is_empty()
+                if not self._overrides_marker_intersection.intersect(
+                    dep.marker
+                ).is_empty()
             ]
             if len(deps) < 2:
                 if not deps or (len(deps) == 1 and deps[0].constraint.is_empty()):
diff --git a/tests/puzzle/test_solver.py b/tests/puzzle/test_solver.py
index 944ef80d58c..6159f389630 100644
--- a/tests/puzzle/test_solver.py
+++ b/tests/puzzle/test_solver.py
@@ -58,7 +58,7 @@
 
 def set_package_python_versions(provider: Provider, python_versions: str) -> None:
     provider._package.python_versions = python_versions
-    provider._python_constraint = provider._package.python_constraint
+    provider._package_python_constraint = provider._package.python_constraint
 
 
 def check_solver_result(
@@ -4402,6 +4402,72 @@ def patched_choose_next(unsatisfied: list[Dependency]) -> Dependency:
     )
 
 
+@pytest.mark.parametrize("numpy_before_pandas", [False, True])
+@pytest.mark.parametrize("conflict", [False, True])
+def test_solver_should_not_raise_errors_for_irrelevant_transitive_python_constraints2(
+    solver: Solver,
+    repo: Repository,
+    package: ProjectPackage,
+    mocker: MockerFixture,
+    numpy_before_pandas: bool,
+    conflict: bool,
+) -> None:
+    """This time with overrides."""
+    package.python_versions = ">=3.6.2, <3.10"
+    set_package_python_versions(solver.provider, ">=3.6.2, <3.10")
+    package.add_dependency(Factory.create_dependency("pandas", ">=1"))
+    package.add_dependency(
+        Factory.create_dependency("numpy", {"version": ">=1.20.0", "python": ">=3.7"})
+    )
+    package.add_dependency(
+        Factory.create_dependency("numpy", {"version": "*", "python": "<3.7"})
+    )
+
+    pandas = get_package("pandas", "1.1.5")
+    pandas.add_dependency(Factory.create_dependency("numpy", ">=1.15"))
+
+    numpy_19 = get_package("numpy", "1.19")
+    numpy_19.python_versions = ">=3.6"
+    numpy_20 = get_package("numpy", "1.20")
+    numpy_20.python_versions = ">=3.8" if conflict else ">=3.7"
+
+    repo.add_package(pandas)
+    repo.add_package(numpy_19)
+    repo.add_package(numpy_20)
+
+    def patched_choose_next(unsatisfied: list[Dependency]) -> Dependency:
+        order = (
+            ("root", "pandas", "numpy")
+            if numpy_before_pandas
+            else ("root", "numpy", "pandas")
+        )
+        for preferred in order:
+            for dep in unsatisfied:
+                if dep.name == preferred:
+                    return dep
+        raise RuntimeError
+
+    mocker.patch(
+        "poetry.mixology.version_solver.VersionSolver._choose_next",
+        side_effect=patched_choose_next,
+    )
+
+    if conflict:
+        with pytest.raises(SolverProblemError):
+            solver.solve()
+    else:
+        transaction = solver.solve()
+
+        check_solver_result(
+            transaction,
+            [
+                {"job": "install", "package": numpy_19},
+                {"job": "install", "package": numpy_20},
+                {"job": "install", "package": pandas},
+            ],
+        )
+
+
 @pytest.mark.parametrize("is_locked", [False, True])
 def test_solver_keeps_multiple_locked_dependencies_for_same_package(
     package: ProjectPackage,