How can I guarantee that my matplotlib axes have their own class?

Question

I have my own class of shapes, and I would like to make sure that all the axes associated with it, created with subplots()or twinx(), etc., have custom behavior.

Now I am doing this by linking new methods to each axis after its creation, for example. using

import types

def my_ax_method(ax, test):
    print('{0} is doing something new as a {1}.'.format(ax, test))

class MyFigure(matplotlib.figure.Figure):
    def __init__(self, **kwargs):
        super(MyFigure, self).__init__(**kwargs)            
        axes_a = None
        axes_b = None
        axes_c = None

    def setup_axes(self, ax):    
        self.axes_a =  ax
        self.axes_b = self.axes_a.twinx()
        self.axes_c = self.axes_a.twiny()    
        self.axes_a.my_method = types.MethodType(my_ax_method, self.axes_a)
        self.axes_b.my_method = types.MethodType(my_ax_method, self.axes_b)
        self.axes_c.my_method = types.MethodType(my_ax_method, self.axes_c)

in something like

    fig, ax = matplotlib.pyplot.subplots(FigureClass=MyFigure)
    fig.setup_axes(ax)

    fig.axes_a.my_method("probe of A")
    fig.axes_b.my_method("test of B")
    fig.axes_c.my_method("trial of C")

This seems like a fragile way to accomplish what I'm trying to do. Is there a better, more Putin way to do this?

In particular, is there a way to ensure that all of Axesmy custom classes Figurebelong to a specific class ( as is done for the shapes themselves ): a custom Axesclass that could use these methods as part of its definition?