継承が必要な各クラスでは、子クラスの開始時に初期化が必要な各クラスのループを実行できます...コピーできる例の方が理解しやすいかもしれません...
class Female_Grandparent:
    def __init__(self):
        self.grandma_name = 'Grandma'
class Male_Grandparent:
    def __init__(self):
        self.grandpa_name = 'Grandpa'
class Parent(Female_Grandparent, Male_Grandparent):
    def __init__(self):
        Female_Grandparent.__init__(self)
        Male_Grandparent.__init__(self)
        self.parent_name = 'Parent Class'
class Child(Parent):
    def __init__(self):
        Parent.__init__(self)
#---------------------------------------------------------------------------------------#
        for cls in Parent.__bases__: # This block grabs the classes of the child
             cls.__init__(self)      # class (which is named 'Parent' in this case), 
                                     # and iterates through them, initiating each one.
                                     # The result is that each parent, of each child,
                                     # is automatically handled upon initiation of the 
                                     # dependent class. WOOT WOOT! :D
#---------------------------------------------------------------------------------------#
g = Female_Grandparent()
print g.grandma_name
p = Parent()
print p.grandma_name
child = Child()
print child.grandma_name