How to inherit from multiple base test classes using pythons unittest?

I'm writing some tests and want to share setUp and tearDown methods between different TestCase classes. To do this I figured you can use a base test class which only implements the setUp and tearDown methods and inherit from it. However, I also have situations where I'd like to use variables from multiple setUp's. Here's an example:

class Base(unittest.TestCase):
    def setUp(self):
        self.shared = 'I am shared between everyone'

    def tearDown(self):
        del self.shared


class Base2(unittest.TestCase):
    def setUp(self):
        self.partial_shared = 'I am shared between only some tests'

    def tearDown(self):
        del self.partial_shared


class Test1(Base):

    def test(self):
        print self.shared
        test_var = 'I only need Base'
        print test_var



class Test2(Base2):

    def test(self):
        print self.partial_shared
        test_var = 'I only need Base2'


class Test3(Base, Base2):

    def test(self):
        test_var = 'I need both Base and Base2'
        print self.shared
        print self.partial_shared


if __name__=='__main__':
    unittest.main()

Here is the output:

..EI am shared between everyone
I only need Base
I am shared between only some tests
I am shared between everyone

======================================================================
ERROR: test (__main__.Test3)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/b3053674/Documents/PyCoTools/PyCoTools/Tests/base_tests.py", line 134, in test
    print self.partial_shared
AttributeError: 'Test3' object has no attribute 'partial_shared'

----------------------------------------------------------------------
Ran 3 tests in 0.004s

FAILED (errors=1)

Is it possible to implement a class heirachy such as this?