diff --git a/CHANGES b/CHANGES
index d6b4135b9f0..d15819da529 100644
--- a/CHANGES
+++ b/CHANGES
@@ -15,6 +15,9 @@ Deprecated
 Features added
 --------------
 
+* #8107: autodoc: Add ``class-doc-from`` option to :rst:dir:`autoclass`
+  directive to control the content of the specific class like
+  :confval:`autoclass_content`
 * #9129: html search: Show search summaries when html_copy_source = False
 * #9120: html theme: Eliminate prompt characters of code-block from copyable
   text
@@ -24,6 +27,7 @@ Features added
 Bugs fixed
 ----------
 
+* #8872: autodoc: stacked singledispatches are wrongly rendered
 * #8597: autodoc: a docsting having metadata only should be treated as
   undocumented
 
diff --git a/doc/usage/extensions/autodoc.rst b/doc/usage/extensions/autodoc.rst
index da0ff7c994c..13a2b30107f 100644
--- a/doc/usage/extensions/autodoc.rst
+++ b/doc/usage/extensions/autodoc.rst
@@ -343,6 +343,10 @@ inserting them into the page source under a suitable :rst:dir:`py:module`,
 
         .. autoclass:: module.name::Noodle
 
+   * :rst:dir:`autoclass` also recognizes the ``class-doc-from`` option that
+     can be used to override the global value of :confval:`autoclass_content`.
+
+     .. versionadded:: 4.1
 
 .. rst:directive:: autofunction
                    autodecorator
@@ -507,7 +511,7 @@ There are also config values that you can set:
    The supported options are ``'members'``, ``'member-order'``,
    ``'undoc-members'``, ``'private-members'``, ``'special-members'``,
    ``'inherited-members'``, ``'show-inheritance'``, ``'ignore-module-all'``,
-   ``'imported-members'`` and ``'exclude-members'``.
+   ``'imported-members'``, ``'exclude-members'`` and ``'class-doc-from'``.
 
    .. versionadded:: 1.8
 
@@ -517,6 +521,9 @@ There are also config values that you can set:
    .. versionchanged:: 2.1
       Added ``'imported-members'``.
 
+   .. versionchanged:: 4.1
+      Added ``'class-doc-from'``.
+
 .. confval:: autodoc_docstring_signature
 
    Functions imported from C modules cannot be introspected, and therefore the
diff --git a/setup.py b/setup.py
index b669afc00e3..7ce37f9eaf8 100644
--- a/setup.py
+++ b/setup.py
@@ -21,7 +21,8 @@
     'sphinxcontrib-htmlhelp',
     'sphinxcontrib-serializinghtml',
     'sphinxcontrib-qthelp',
-    'Jinja2>=2.3',
+    'Jinja2>=2.3,<3.0',
+    'MarkupSafe<2.0',
     'Pygments>=2.0',
     'docutils>=0.14,<0.18',
     'snowballstemmer>=1.1',
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 962ba2ad0bf..ff6475c9442 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -129,6 +129,14 @@ def member_order_option(arg: Any) -> Optional[str]:
         raise ValueError(__('invalid value for member-order option: %s') % arg)
 
 
+def class_doc_from_option(arg: Any) -> Optional[str]:
+    """Used to convert the :class-doc-from: option to autoclass directives."""
+    if arg in ('both', 'class', 'init'):
+        return arg
+    else:
+        raise ValueError(__('invalid value for class-doc-from option: %s') % arg)
+
+
 SUPPRESS = object()
 
 
@@ -1320,12 +1328,12 @@ def format_signature(self, **kwargs: Any) -> str:
                 if typ is object:
                     pass  # default implementation. skipped.
                 else:
-                    self.annotate_to_first_argument(func, typ)
-
-                    documenter = FunctionDocumenter(self.directive, '')
-                    documenter.object = func
-                    documenter.objpath = [None]
-                    sigs.append(documenter.format_signature())
+                    dispatchfunc = self.annotate_to_first_argument(func, typ)
+                    if dispatchfunc:
+                        documenter = FunctionDocumenter(self.directive, '')
+                        documenter.object = dispatchfunc
+                        documenter.objpath = [None]
+                        sigs.append(documenter.format_signature())
         if overloaded:
             actual = inspect.signature(self.object,
                                        type_aliases=self.config.autodoc_type_aliases)
@@ -1350,28 +1358,34 @@ def merge_default_value(self, actual: Signature, overload: Signature) -> Signatu
 
         return overload.replace(parameters=parameters)
 
-    def annotate_to_first_argument(self, func: Callable, typ: Type) -> None:
+    def annotate_to_first_argument(self, func: Callable, typ: Type) -> Optional[Callable]:
         """Annotate type hint to the first argument of function if needed."""
         try:
             sig = inspect.signature(func, type_aliases=self.config.autodoc_type_aliases)
         except TypeError as exc:
             logger.warning(__("Failed to get a function signature for %s: %s"),
                            self.fullname, exc)
-            return
+            return None
         except ValueError:
-            return
+            return None
 
         if len(sig.parameters) == 0:
-            return
+            return None
+
+        def dummy():
+            pass
 
         params = list(sig.parameters.values())
         if params[0].annotation is Parameter.empty:
             params[0] = params[0].replace(annotation=typ)
             try:
-                func.__signature__ = sig.replace(parameters=params)  # type: ignore
+                dummy.__signature__ = sig.replace(parameters=params)  # type: ignore
+                return dummy
             except (AttributeError, TypeError):
                 # failed to update signature (ex. built-in or extension types)
-                return
+                return None
+        else:
+            return None
 
 
 class DecoratorDocumenter(FunctionDocumenter):
@@ -1417,6 +1431,7 @@ class ClassDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):  # type:
         'show-inheritance': bool_option, 'member-order': member_order_option,
         'exclude-members': exclude_members_option,
         'private-members': members_option, 'special-members': members_option,
+        'class-doc-from': class_doc_from_option,
     }
 
     _signature_class: Any = None
@@ -1651,7 +1666,7 @@ def get_doc(self, ignore: int = None) -> Optional[List[List[str]]]:
         if lines is not None:
             return lines
 
-        content = self.config.autoclass_content
+        classdoc_from = self.options.get('class-doc-from', self.config.autoclass_content)
 
         docstrings = []
         attrdocstring = self.get_attr(self.object, '__doc__', None)
@@ -1660,7 +1675,7 @@ def get_doc(self, ignore: int = None) -> Optional[List[List[str]]]:
 
         # for classes, what the "docstring" is can be controlled via a
         # config value; the default is only the class docstring
-        if content in ('both', 'init'):
+        if classdoc_from in ('both', 'init'):
             __init__ = self.get_attr(self.object, '__init__', None)
             initdocstring = getdoc(__init__, self.get_attr,
                                    self.config.autodoc_inherit_docstrings,
@@ -1682,7 +1697,7 @@ def get_doc(self, ignore: int = None) -> Optional[List[List[str]]]:
                      initdocstring.strip() == object.__new__.__doc__)):  # for !pypy
                     initdocstring = None
             if initdocstring:
-                if content == 'init':
+                if classdoc_from == 'init':
                     docstrings = [initdocstring]
                 else:
                     docstrings.append(initdocstring)
@@ -2109,13 +2124,13 @@ def format_signature(self, **kwargs: Any) -> str:
                 if typ is object:
                     pass  # default implementation. skipped.
                 else:
-                    self.annotate_to_first_argument(func, typ)
-
-                    documenter = MethodDocumenter(self.directive, '')
-                    documenter.parent = self.parent
-                    documenter.object = func
-                    documenter.objpath = [None]
-                    sigs.append(documenter.format_signature())
+                    dispatchmeth = self.annotate_to_first_argument(func, typ)
+                    if dispatchmeth:
+                        documenter = MethodDocumenter(self.directive, '')
+                        documenter.parent = self.parent
+                        documenter.object = dispatchmeth
+                        documenter.objpath = [None]
+                        sigs.append(documenter.format_signature())
         if overloaded:
             if inspect.isstaticmethod(self.object, cls=self.parent, name=self.object_name):
                 actual = inspect.signature(self.object, bound_method=False,
@@ -2149,27 +2164,34 @@ def merge_default_value(self, actual: Signature, overload: Signature) -> Signatu
 
         return overload.replace(parameters=parameters)
 
-    def annotate_to_first_argument(self, func: Callable, typ: Type) -> None:
+    def annotate_to_first_argument(self, func: Callable, typ: Type) -> Optional[Callable]:
         """Annotate type hint to the first argument of function if needed."""
         try:
             sig = inspect.signature(func, type_aliases=self.config.autodoc_type_aliases)
         except TypeError as exc:
             logger.warning(__("Failed to get a method signature for %s: %s"),
                            self.fullname, exc)
-            return
+            return None
         except ValueError:
-            return
+            return None
+
         if len(sig.parameters) == 1:
-            return
+            return None
+
+        def dummy():
+            pass
 
         params = list(sig.parameters.values())
         if params[1].annotation is Parameter.empty:
             params[1] = params[1].replace(annotation=typ)
             try:
-                func.__signature__ = sig.replace(parameters=params)  # type: ignore
+                dummy.__signature__ = sig.replace(parameters=params)  # type: ignore
+                return dummy
             except (AttributeError, TypeError):
                 # failed to update signature (ex. built-in or extension types)
-                return
+                return None
+        else:
+            return None
 
 
 class NonDataDescriptorMixin(DataDocumenterMixinBase):
diff --git a/sphinx/ext/autodoc/directive.py b/sphinx/ext/autodoc/directive.py
index c58d0c41181..a554adf688b 100644
--- a/sphinx/ext/autodoc/directive.py
+++ b/sphinx/ext/autodoc/directive.py
@@ -30,7 +30,7 @@
 AUTODOC_DEFAULT_OPTIONS = ['members', 'undoc-members', 'inherited-members',
                            'show-inheritance', 'private-members', 'special-members',
                            'ignore-module-all', 'exclude-members', 'member-order',
-                           'imported-members']
+                           'imported-members', 'class-doc-from']
 
 AUTODOC_EXTENDABLE_OPTIONS = ['members', 'private-members', 'special-members',
                               'exclude-members']
diff --git a/tests/roots/test-ext-autodoc/target/singledispatch.py b/tests/roots/test-ext-autodoc/target/singledispatch.py
index 3fa81dcae4c..fca2b668381 100644
--- a/tests/roots/test-ext-autodoc/target/singledispatch.py
+++ b/tests/roots/test-ext-autodoc/target/singledispatch.py
@@ -15,6 +15,7 @@ def func(arg, kwarg=None):
 
 
 @func.register(int)
+@func.register(float)
 def _func_int(arg, kwarg=None):
     """A function for int."""
     pass
diff --git a/tests/roots/test-ext-autodoc/target/singledispatchmethod.py b/tests/roots/test-ext-autodoc/target/singledispatchmethod.py
index b5ccbb2f09d..086c7fe668d 100644
--- a/tests/roots/test-ext-autodoc/target/singledispatchmethod.py
+++ b/tests/roots/test-ext-autodoc/target/singledispatchmethod.py
@@ -10,6 +10,7 @@ def meth(self, arg, kwarg=None):
         pass
 
     @meth.register(int)
+    @meth.register(float)
     def _meth_int(self, arg, kwarg=None):
         """A method for int."""
         pass
diff --git a/tests/test_ext_autodoc.py b/tests/test_ext_autodoc.py
index fcaafa2af4b..4c16886b3fc 100644
--- a/tests/test_ext_autodoc.py
+++ b/tests/test_ext_autodoc.py
@@ -2108,6 +2108,7 @@ def test_singledispatch(app):
         '',
         '',
         '.. py:function:: func(arg, kwarg=None)',
+        '                 func(arg: float, kwarg=None)',
         '                 func(arg: int, kwarg=None)',
         '                 func(arg: str, kwarg=None)',
         '   :module: target.singledispatch',
@@ -2135,6 +2136,7 @@ def test_singledispatchmethod(app):
         '',
         '',
         '   .. py:method:: Foo.meth(arg, kwarg=None)',
+        '                  Foo.meth(arg: float, kwarg=None)',
         '                  Foo.meth(arg: int, kwarg=None)',
         '                  Foo.meth(arg: str, kwarg=None)',
         '      :module: target.singledispatchmethod',
@@ -2153,6 +2155,7 @@ def test_singledispatchmethod_automethod(app):
     assert list(actual) == [
         '',
         '.. py:method:: Foo.meth(arg, kwarg=None)',
+        '               Foo.meth(arg: float, kwarg=None)',
         '               Foo.meth(arg: int, kwarg=None)',
         '               Foo.meth(arg: str, kwarg=None)',
         '   :module: target.singledispatchmethod',
diff --git a/tests/test_ext_autodoc_autoclass.py b/tests/test_ext_autodoc_autoclass.py
index d879f8e1491..096dc939738 100644
--- a/tests/test_ext_autodoc_autoclass.py
+++ b/tests/test_ext_autodoc_autoclass.py
@@ -264,6 +264,53 @@ def test_show_inheritance_for_subclass_of_generic_type(app):
     ]
 
 
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_class_doc_from_class(app):
+    options = {"members": None,
+               "class-doc-from": "class"}
+    actual = do_autodoc(app, 'class', 'target.autoclass_content.C', options)
+    assert list(actual) == [
+        '',
+        '.. py:class:: C()',
+        '   :module: target.autoclass_content',
+        '',
+        '   A class having __init__, no __new__',
+        '',
+    ]
+
+
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_class_doc_from_init(app):
+    options = {"members": None,
+               "class-doc-from": "init"}
+    actual = do_autodoc(app, 'class', 'target.autoclass_content.C', options)
+    assert list(actual) == [
+        '',
+        '.. py:class:: C()',
+        '   :module: target.autoclass_content',
+        '',
+        '   __init__ docstring',
+        '',
+    ]
+
+
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_class_doc_from_both(app):
+    options = {"members": None,
+               "class-doc-from": "both"}
+    actual = do_autodoc(app, 'class', 'target.autoclass_content.C', options)
+    assert list(actual) == [
+        '',
+        '.. py:class:: C()',
+        '   :module: target.autoclass_content',
+        '',
+        '   A class having __init__, no __new__',
+        '',
+        '   __init__ docstring',
+        '',
+    ]
+
+
 def test_class_alias(app):
     def autodoc_process_docstring(*args):
         """A handler always raises an error.
diff --git a/tests/test_ext_autodoc_autofunction.py b/tests/test_ext_autodoc_autofunction.py
index 6150918894c..ca2429b5e88 100644
--- a/tests/test_ext_autodoc_autofunction.py
+++ b/tests/test_ext_autodoc_autofunction.py
@@ -119,6 +119,7 @@ def test_singledispatch(app):
     assert list(actual) == [
         '',
         '.. py:function:: func(arg, kwarg=None)',
+        '                 func(arg: float, kwarg=None)',
         '                 func(arg: int, kwarg=None)',
         '                 func(arg: str, kwarg=None)',
         '   :module: target.singledispatch',