diff --git a/README.md b/README.md
index 0c49e0f..9539620 100644
--- a/README.md
+++ b/README.md
@@ -88,12 +88,13 @@ from asdf.extension import Extension
 from asdf_pydantic.converter import AsdfPydanticConverter
 from mypackage.shapes import Rectangle
 
-AsdfPydanticConverter.add_models(Rectangle)
+converter = AsdfPydanticConverter()
+converter.add_models(Rectangle)
 
 class ShapesExtension(Extension):
     extension_uri = "asdf://asdf-pydantic/examples/extensions/shapes-1.0.0"
-    converters = [AsdfPydanticConverter()]
-    tags = [*AsdfPydanticConverter().tags]
+    converters = [converter]
+    tags = [*converter.tags]
 ```
 
 Install the extension either by entry point specification or add it to
diff --git a/asdf_pydantic/converter.py b/asdf_pydantic/converter.py
index 7100044..4be2684 100644
--- a/asdf_pydantic/converter.py
+++ b/asdf_pydantic/converter.py
@@ -1,37 +1,29 @@
 from __future__ import annotations
 
-from typing import Optional, Type
+from typing import Type
 
 from asdf.extension import Converter
 
 from asdf_pydantic.model import AsdfPydanticModel
 
-_ASDF_PYDANTIC_SINGLETON_CONVERTER: Optional[AsdfPydanticConverter] = None
-
 
 class AsdfPydanticConverter(Converter):
-    """Implements a converter compatible with all subclass of AsdfPydanticModel.
-
-    The instance is a singleton.
-    """
-
-    _tag_to_class: dict[str, Type[AsdfPydanticModel]] = {}
+    """Implements a converter compatible with all subclass of AsdfPydanticModel."""
 
-    def __init__(self) -> None:
-        global _ASDF_PYDANTIC_SINGLETON_CONVERTER
+    _tag_to_class: dict[str, Type[AsdfPydanticModel]]
 
-        if _ASDF_PYDANTIC_SINGLETON_CONVERTER is None:
-            _ASDF_PYDANTIC_SINGLETON_CONVERTER = self
+    def __init__(self, *model_classes: Type[AsdfPydanticModel]) -> None:
+        self._tag_to_class = {}
+        self.add_models(*model_classes)
+        super().__init__()
 
-        self = _ASDF_PYDANTIC_SINGLETON_CONVERTER
-
-    @classmethod
     def add_models(
-        cls, *model_classes: Type[AsdfPydanticModel]
+        self, *model_classes: Type[AsdfPydanticModel]
     ) -> "AsdfPydanticConverter":
         for model_class in model_classes:
-            cls._tag_to_class[model_class.get_tag_uri()] = model_class
-        return cls()
+            self._tag_to_class[model_class.get_tag_uri()] = model_class
+
+        return self
 
     @property
     def tags(self) -> tuple[str]:
diff --git a/tests/examples/test_astropy_tables.py b/tests/examples/test_astropy_tables.py
index d90bd4a..c64ae05 100644
--- a/tests/examples/test_astropy_tables.py
+++ b/tests/examples/test_astropy_tables.py
@@ -24,13 +24,14 @@ class Database(AsdfPydanticModel):
 @pytest.fixture()
 def asdf_extension():
     """Registers an ASDF extension containing models for this test."""
-    AsdfPydanticConverter.add_models(Database)
+    converter = AsdfPydanticConverter()
+    converter.add_models(Database)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"
 
-        converters = [AsdfPydanticConverter()]  # type: ignore
-        tags = [*AsdfPydanticConverter().tags]  # type: ignore
+        converters = [converter]  # type: ignore
+        tags = [*converter.tags]  # type: ignore
 
     asdf.get_config().add_extension(TestExtension())
 
diff --git a/tests/examples/test_node.py b/tests/examples/test_node.py
index 09cdb6d..5408af8 100644
--- a/tests/examples/test_node.py
+++ b/tests/examples/test_node.py
@@ -54,12 +54,13 @@ class AsdfNode(AsdfPydanticModel):
 @pytest.fixture()
 def asdf_extension():
     """Registers an ASDF extension containing models for this test."""
-    AsdfPydanticConverter.add_models(AsdfNode)
+    converter = AsdfPydanticConverter()
+    converter.add_models(AsdfNode)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"
 
-        converters = [AsdfPydanticConverter()]  # type: ignore
+        converters = [converter]  # type: ignore
         tags = [AsdfNode.get_tag_definition()]  # type: ignore
 
     with asdf.config_context() as asdf_config:
diff --git a/tests/examples/test_rectangle.py b/tests/examples/test_rectangle.py
index 9d414d7..793a9fe 100644
--- a/tests/examples/test_rectangle.py
+++ b/tests/examples/test_rectangle.py
@@ -14,12 +14,13 @@
 @pytest.fixture()
 def asdf_extension():
     """Registers an ASDF extension containing models for this test."""
-    AsdfPydanticConverter.add_models(AsdfRectangle)
+    converter = AsdfPydanticConverter()
+    converter.add_models(AsdfRectangle)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"
 
-        converters = [AsdfPydanticConverter()]  # type: ignore
+        converters = [converter]  # type: ignore
         tags = [AsdfRectangle.get_tag_definition()]  # type: ignore
 
     with asdf.config_context() as asdf_config:
diff --git a/tests/patterns/astropy_types_test.py b/tests/patterns/astropy_types_test.py
index 4c35af4..4106ee4 100644
--- a/tests/patterns/astropy_types_test.py
+++ b/tests/patterns/astropy_types_test.py
@@ -23,13 +23,14 @@ class DataContainer(AsdfPydanticModel):
 
 
 def setup_module():
-    AsdfPydanticConverter.add_models(DataPoint, DataContainer)
+    converter = AsdfPydanticConverter()
+    converter.add_models(DataPoint, DataContainer)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"
 
-        converters = [AsdfPydanticConverter()]  # type: ignore
-        tags = [*AsdfPydanticConverter().tags]  # type: ignore
+        converters = [converter]  # type: ignore
+        tags = [*converter.tags]  # type: ignore
 
     asdf.get_config().add_extension(TestExtension())
 
diff --git a/tests/patterns/union_type_test.py b/tests/patterns/union_type_test.py
index f10d27c..98f1da5 100644
--- a/tests/patterns/union_type_test.py
+++ b/tests/patterns/union_type_test.py
@@ -20,13 +20,14 @@ class UnionObject(AsdfPydanticModel):
 
 
 def setup_module():
-    AsdfPydanticConverter.add_models(UnionObject)
+    converter = AsdfPydanticConverter()
+    converter.add_models(UnionObject)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"
 
-        converters = [AsdfPydanticConverter()]  # type: ignore
-        tags = [*AsdfPydanticConverter().tags]  # type: ignore
+        converters = [converter]  # type: ignore
+        tags = [*converter.tags]  # type: ignore
 
     asdf.get_config().add_extension(TestExtension())
 
diff --git a/tests/schema_validation_test.py b/tests/schema_validation_test.py
index 60a3f09..2508462 100644
--- a/tests/schema_validation_test.py
+++ b/tests/schema_validation_test.py
@@ -14,13 +14,14 @@
 
 
 def setup_module():
-    AsdfPydanticConverter.add_models(AsdfRectangle)
+    converter = AsdfPydanticConverter()
+    converter.add_models(AsdfRectangle)
 
     class TestExtension(Extension):
         extension_uri = "asdf://asdf-pydantic/examples/extensions/test-1.0.0"  # type: ignore
 
-        tags = [*AsdfPydanticConverter().tags]  # type: ignore
-        converters = [AsdfPydanticConverter()]  # type: ignore
+        tags = [*converter.tags]  # type: ignore
+        converters = [converter]  # type: ignore
 
     # HACK: The schema URI should be referenced from `AsdfRectangle._schema`.
     # Then there should be a way to automatically add the schema to ASDF
diff --git a/tests/test_converter.py b/tests/test_converter.py
new file mode 100644
index 0000000..5421296
--- /dev/null
+++ b/tests/test_converter.py
@@ -0,0 +1,13 @@
+import pytest
+
+from asdf_pydantic.converter import AsdfPydanticConverter
+from asdf_pydantic.model import AsdfPydanticModel
+
+
+class TestModel(AsdfPydanticModel):
+    _tag = "https://example.org/test_model"
+
+
+@pytest.mark.parametrize("args", [tuple(), (TestModel,)])
+def test_converter_is_unscoped_by_default(args):
+    assert AsdfPydanticConverter(*args) is not AsdfPydanticConverter(*args)