Q:

__bases__ doesn't work! What's next?

The following code doesn't work in Python 3.x, but it used to work with old-style classes:
class Extender:
    def extension(self):
        print("Some work...")

class Base:
    pass

Base.__bases__ += (Extender,)

Base().extension()

Question is simple: How can I add dynamically (at runtime) a super class to a class in Python 3.x?
But I'm ready the answer will be hard! )

A:

As for me it is impossible. But you can create new class dynamically:
class Extender(object):
    def extension(self):
        print("Some work...")

class Base(object):
    pass

Base = type('Base', (Base, Extender, object), {})
Base().extension()

A:

It appears that it is possible to dynamically change Base.__bases__
if Base.__base__ is not object. (By dynamically change, I mean in such a way that all pre-existing instances that inherit from Base also get dynamically changed. Otherwise see Mykola Kharechko's solution).
If Base.__base__ is some dummy class TopBase, then assignment to Base.__bases__ seems to work:
class Extender(object):
    def extension(self):
        print("Some work...")

class TopBase(object):
    pass

class Base(TopBase):
    pass

b=Base()
print(Base.__bases__)
# (<class '__main__.TopBase'>,)

Base.__bases__ += (Extender,)
print(Base.__bases__)
# (<class '__main__.TopBase'>, <class '__main__.Extender'>)
Base().extension()
# Some work...
b.extension()
# Some work...

Base.__bases__ = (Extender, TopBase) 
print(Base.__bases__)
# (<class '__main__.Extender'>, <class '__main__.TopBase'>)
Base().extension()
# Some work...
b.extension()
# Some work...

This was tested to work in Python 2 (for new- and old-style classes) and for Python 3. I have no idea why it works while this does not:
class Extender(object):
    def extension(self):
        print("Some work...")

class Base(object):
    pass

Base.__bases__ = (Extender, object)
# TypeError: __bases__ assignment: 'Extender' deallocator differs from 'object'

