diff --git a/marshmallow_dataclass/__init__.py b/marshmallow_dataclass/__init__.py
index 7ad8da5..ac3d251 100644
--- a/marshmallow_dataclass/__init__.py
+++ b/marshmallow_dataclass/__init__.py
@@ -68,7 +68,6 @@ class User:
 
 from marshmallow_dataclass.lazy_class_attribute import lazy_class_attribute
 
-
 if sys.version_info >= (3, 11):
     from typing import dataclass_transform
 elif sys.version_info >= (3, 7):
@@ -480,20 +479,35 @@ def _field_by_supertype(
         )
 
 
+COLLECTIONS_TYPES: Dict[str, Set[Type]] = {
+    "list": {list, List},
+    "dict": {dict, Dict},
+    "mapping": {Mapping, collections.abc.Mapping},
+    "sequence": {Sequence, collections.abc.Sequence},
+    "set": {set, Set, collections.abc.Set},
+    "frozenset": {frozenset, FrozenSet},
+    "tuple": {tuple, Tuple},
+}
+
+
 def _generic_type_add_any(typ: type) -> type:
     """if typ is generic type without arguments, replace them by Any."""
-    if typ in (list, List):
-        typ = List[Any]
-    elif typ in (dict, Dict):
-        typ = Dict[Any, Any]
-    elif typ in (Mapping, collections.abc.Mapping):
-        typ = Mapping[Any, Any]
-    elif typ in (Sequence, collections.abc.Sequence):
-        typ = Sequence[Any]
-    elif typ in (set, Set, collections.abc.Set):
-        typ = Set[Any]
-    elif typ in (frozenset, FrozenSet):
-        typ = FrozenSet[Any]
+    args = typing_inspect.get_args(typ)
+    if not args or any(typing_inspect.is_typevar(arg) for arg in args):
+        if typ in COLLECTIONS_TYPES["list"]:
+            typ = List[Any]
+        elif typ in COLLECTIONS_TYPES["dict"]:
+            typ = Dict[Any, Any]
+        elif typ in COLLECTIONS_TYPES["mapping"]:
+            typ = Mapping[Any, Any]
+        elif typ in COLLECTIONS_TYPES["sequence"]:
+            typ = Sequence[Any]
+        elif typ in COLLECTIONS_TYPES["set"]:
+            typ = Set[Any]
+        elif typ in COLLECTIONS_TYPES["frozenset"]:
+            typ = FrozenSet[Any]
+        elif typ in COLLECTIONS_TYPES["tuple"]:
+            typ = Tuple[Any, ...]
     return typ
 
 
@@ -512,7 +526,7 @@ def _field_for_generic_type(
         # Override base_schema.TYPE_MAPPING to change the class used for generic types below
         type_mapping = base_schema.TYPE_MAPPING if base_schema else {}
 
-        if origin in (list, List):
+        if origin in COLLECTIONS_TYPES["list"]:
             child_type = field_for_schema(
                 arguments[0], base_schema=base_schema, typ_frame=typ_frame
             )
@@ -521,8 +535,8 @@ def _field_for_generic_type(
                 type_mapping.get(List, marshmallow.fields.List),
             )
             return list_type(child_type, **metadata)
-        if origin in (collections.abc.Sequence, Sequence) or (
-            origin in (tuple, Tuple)
+        if origin in COLLECTIONS_TYPES["sequence"] or (
+            origin in COLLECTIONS_TYPES["tuple"]
             and len(arguments) == 2
             and arguments[1] is Ellipsis
         ):
@@ -532,7 +546,7 @@ def _field_for_generic_type(
                 arguments[0], base_schema=base_schema, typ_frame=typ_frame
             )
             return collection_field.Sequence(cls_or_instance=child_type, **metadata)
-        if origin in (set, Set):
+        if origin in COLLECTIONS_TYPES["set"]:
             from . import collection_field
 
             child_type = field_for_schema(
@@ -541,7 +555,7 @@ def _field_for_generic_type(
             return collection_field.Set(
                 cls_or_instance=child_type, frozen=False, **metadata
             )
-        if origin in (frozenset, FrozenSet):
+        if origin in COLLECTIONS_TYPES["frozenset"]:
             from . import collection_field
 
             child_type = field_for_schema(
@@ -550,7 +564,7 @@ def _field_for_generic_type(
             return collection_field.Set(
                 cls_or_instance=child_type, frozen=True, **metadata
             )
-        if origin in (tuple, Tuple):
+        if origin in COLLECTIONS_TYPES["tuple"]:
             children = tuple(
                 field_for_schema(arg, base_schema=base_schema, typ_frame=typ_frame)
                 for arg in arguments
@@ -562,7 +576,7 @@ def _field_for_generic_type(
                 ),
             )
             return tuple_type(children, **metadata)
-        elif origin in (dict, Dict, collections.abc.Mapping, Mapping):
+        elif origin in COLLECTIONS_TYPES["dict"] | COLLECTIONS_TYPES["mapping"]:
             dict_type = type_mapping.get(Dict, marshmallow.fields.Dict)
             return dict_type(
                 keys=field_for_schema(
@@ -727,7 +741,7 @@ def field_for_schema(
         )
 
     # enumerations
-    if issubclass(typ, Enum):
+    if isinstance(typ, type) and issubclass(typ, Enum):
         try:
             return marshmallow.fields.Enum(typ, **metadata)
         except AttributeError: