diff --git a/luigi/parameter.py b/luigi/parameter.py
index 9f1ae104d3..bc06127721 100644
--- a/luigi/parameter.py
+++ b/luigi/parameter.py
@@ -142,6 +142,7 @@ class UnconsumedParameterWarning(UserWarning):
 
 
 T = TypeVar("T", default=str)
+_OptT = TypeVar("_OptT")
 
 
 class ConfigPath(TypedDict):
@@ -426,21 +427,31 @@ def _parser_kwargs(cls, param_name, task_name=None):
         }
 
 
-class OptionalParameterMixin:
+class OptionalParameterMixin(Generic[_OptT]):
     """
     Mixin to make a parameter class optional and treat empty string as None.
     """
 
-    expected_type = type(None)
+    expected_type: type = type(None)
+
+    def __init__(
+        self,
+        default: Union[_OptT, None, _NoValueType] = _no_value,
+        **kwargs: Unpack[_ParameterKwargs],
+    ):
+        super().__init__(default=default, **kwargs)  # type: ignore[arg-type, call-arg, misc]
 
     @overload
-    def __get__(self: "Parameter[T]", instance: None, owner: Any) -> "Parameter[Optional[T]]": ...
+    def __get__(self, instance: None, owner: Any) -> "Parameter[Optional[_OptT]]": ...
 
     @overload
-    def __get__(self: "Parameter[T]", instance: Any, owner: Any) -> Optional[T]: ...
+    def __get__(self, instance: Any, owner: Any) -> Optional[_OptT]: ...
 
     def __get__(self, instance: Any, owner: Any) -> Any:
-        return super().__get__(instance, owner)
+        return super().__get__(instance, owner)  # type: ignore[misc]
+
+    def __set__(self, instance: Any, value: Optional[_OptT]):
+        super().__set__(instance, value)  # type: ignore[misc]
 
     def serialize(self, x):
         """
@@ -485,13 +496,13 @@ def next_in_enumeration(self, value):
         return None
 
 
-class OptionalParameter(OptionalParameterMixin, Parameter[Optional[str]]):
+class OptionalParameter(OptionalParameterMixin[str], Parameter[Optional[str]]):
     """Class to parse optional parameters."""
 
     expected_type = str
 
 
-class OptionalStrParameter(OptionalParameterMixin, Parameter[Optional[str]]):
+class OptionalStrParameter(OptionalParameterMixin[str], Parameter[Optional[str]]):
     """Class to parse optional str parameters."""
 
     expected_type = str
@@ -798,7 +809,7 @@ def next_in_enumeration(self, value):
         return value + 1
 
 
-class OptionalIntParameter(OptionalParameterMixin, IntParameter):
+class OptionalIntParameter(OptionalParameterMixin[int], IntParameter):  # type: ignore[misc]
     """Class to parse optional int parameters."""
 
     expected_type = int
@@ -816,7 +827,7 @@ def parse(self, x):
         return float(x)
 
 
-class OptionalFloatParameter(OptionalParameterMixin, FloatParameter):
+class OptionalFloatParameter(OptionalParameterMixin[float], FloatParameter):  # type: ignore[misc]
     """Class to parse optional float parameters."""
 
     expected_type = float
@@ -897,7 +908,7 @@ def _parser_kwargs(self, *args, **kwargs):
         return parser_kwargs
 
 
-class OptionalBoolParameter(OptionalParameterMixin, BoolParameter):
+class OptionalBoolParameter(OptionalParameterMixin[bool], BoolParameter):  # type: ignore[misc]
     """Class to parse optional bool parameters."""
 
     expected_type = bool
@@ -1299,7 +1310,7 @@ def serialize(self, x):
         return json.dumps(x, cls=_DictParamEncoder)
 
 
-class OptionalDictParameter(OptionalParameterMixin, DictParameter):
+class OptionalDictParameter(OptionalParameterMixin[FrozenOrderedDict], DictParameter):  # type: ignore[misc]
     """Class to parse optional dict parameters."""
 
     expected_type = FrozenOrderedDict
@@ -1454,7 +1465,7 @@ def serialize(self, x):
         return json.dumps(x, cls=_DictParamEncoder)
 
 
-class OptionalListParameter(OptionalParameterMixin, ListParameter):
+class OptionalListParameter(OptionalParameterMixin[ListT], ListParameter):  # type: ignore[misc]
     """Class to parse optional list parameters."""
 
     expected_type = tuple
@@ -1525,7 +1536,7 @@ def _convert_iterable_to_tuple(self, x):
         return tuple(x)
 
 
-class OptionalTupleParameter(OptionalParameterMixin, TupleParameter):
+class OptionalTupleParameter(OptionalParameterMixin[ListT], TupleParameter):  # type: ignore[misc]
     """Class to parse optional tuple parameters."""
 
     expected_type = tuple
@@ -1588,13 +1599,13 @@ def __init__(
         """
         if var_type is None:
             raise ParameterException("var_type must be specified")
-        self._var_type = var_type
+        self._var_type: Type[NumericalType] = var_type
         if min_value is None:
             raise ParameterException("min_value must be specified")
-        self._min_value = min_value
+        self._min_value: NumericalType = min_value
         if max_value is None:
             raise ParameterException("max_value must be specified")
-        self._max_value = max_value
+        self._max_value: NumericalType = max_value
         self._left_op = left_op
         self._right_op = right_op
         self._permitted_range = "{var_type} in {left_endpoint}{min_value}, {max_value}{right_endpoint}".format(
@@ -1604,7 +1615,7 @@ def __init__(
             left_endpoint="[" if left_op == operator.le else "(",
             right_endpoint=")" if right_op == operator.lt else "]",
         )
-        super().__init__(default=default, **kwargs)
+        super().__init__(default=default, **kwargs)  # type: ignore[arg-type]
         if self.description:
             self.description += " "
         else:
@@ -1619,7 +1630,7 @@ def parse(self, x):
             raise ValueError("{s} is not in the set of {permitted_range}".format(s=x, permitted_range=self._permitted_range))
 
 
-class OptionalNumericalParameter(OptionalParameterMixin, NumericalParameter):
+class OptionalNumericalParameter(OptionalParameterMixin[NumericalType], NumericalParameter[NumericalType]):  # type: ignore[misc]
     """Class to parse optional numerical parameters."""
 
     def __init__(
@@ -1627,7 +1638,7 @@ def __init__(
         default: Union[Optional[NumericalType], _NoValueType] = _no_value,
         **kwargs: Unpack[_ParameterKwargs],
     ):
-        super().__init__(default=default, **kwargs)
+        NumericalParameter.__init__(self, default=default, **kwargs)  # type: ignore[arg-type, misc]
         self.expected_type = self._var_type
 
 
@@ -1664,7 +1675,7 @@ def __init__(
         default: Union[ChoiceType, _NoValueType] = _no_value,
         *,
         choices: Optional[Sequence[ChoiceType]] = None,
-        var_type: Type[ChoiceType] = str,
+        var_type: Type[ChoiceType] = str,  # type: ignore[assignment]
         **kwargs: Unpack[_ParameterKwargs],
     ):
         """
@@ -1726,7 +1737,7 @@ class MyTask(luigi.Task):
 
     _sep = ","
 
-    @overload
+    @overload  # type: ignore[override]
     def __get__(self, instance: None, owner: Any) -> "Parameter[Tuple[ChoiceType, ...]]": ...
 
     @overload
@@ -1738,7 +1749,7 @@ def __get__(self, instance: Any, owner: Any) -> Any:
     def __init__(
         self,
         default: Union[Tuple[ChoiceType, ...], _NoValueType] = _no_value,
-        var_type: Type[ChoiceType] = str,
+        var_type: Type[ChoiceType] = str,  # type: ignore[assignment]
         choices: Optional[Sequence[ChoiceType]] = None,
         **kwargs: Unpack[_ParameterKwargs],
     ):
@@ -1758,17 +1769,17 @@ def serialize(self, x):
         return self._sep.join(x)
 
 
-class OptionalChoiceParameter(OptionalParameterMixin, ChoiceParameter[ChoiceType]):
+class OptionalChoiceParameter(OptionalParameterMixin[ChoiceType], ChoiceParameter[ChoiceType]):  # type: ignore[misc]
     """Class to parse optional choice parameters."""
 
     def __init__(
         self,
         default: Union[Optional[ChoiceType], _NoValueType] = _no_value,
-        var_type: Type[ChoiceType] = str,
+        var_type: Type[ChoiceType] = str,  # type: ignore[assignment]
         choices: Optional[Sequence[ChoiceType]] = None,
         **kwargs: Unpack[_ParameterKwargs],
     ):
-        super().__init__(default=default, var_type=var_type, choices=choices, **kwargs)  # type: ignore[arg-type]
+        ChoiceParameter.__init__(self, default=default, var_type=var_type, choices=choices, **kwargs)  # type: ignore[arg-type, misc]
         self.expected_type = self._var_type
 
 
@@ -1831,7 +1842,7 @@ def normalize(self, x):
         return path
 
 
-class OptionalPathParameter(OptionalParameter, PathParameter):
+class OptionalPathParameter(OptionalParameter, PathParameter):  # type: ignore[misc]
     """Class to parse optional path parameters."""
 
-    expected_type = (str, Path)  # type: ignore
+    expected_type = (str, Path)  # type: ignore[assignment]
diff --git a/pyproject.toml b/pyproject.toml
index 36770fd7eb..a5e2b31275 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -191,7 +191,6 @@ module = [
     "luigi.contrib.sqla",
     "luigi.interface",
     "luigi.notifications",
-    "luigi.parameter",
     "luigi.tools.range",
     "luigi.worker",
 ]