The Python handler supports extensions through mkdocstrings' handler extensions.

Specifically, additional templates can be added to the handler, and Griffe extensions can instruct the handler to use a particular template for a particular object by setting a value in the Griffe object's extra dictionary:

obj = ...  # get a reference to a Griffe object
if "mkdocstrings" not in obj.extra:
    obj.extra["mkdocstrings"] = {}
obj.extra["mkdocstrings"]["template"] = "template_name.html"