How to add X and Y group labels to subplots in a matplotlib plot?

I am making a plot matrix using subplots in matplotlib with a shared x and y axis. What I am looking to do is label the x and y groups similar to how they are labeled in the default JMP graph maker.

In the below image, all of the blue items are what I already have, and the red items are what I am looking to add to the plot.

Take advantage of the titles and axes labels, to avoid conflict with the existing axes, twin them:

import matplotlib.pyplot as plt
fig, axes = plt.subplots(nrows=3, ncols=3,
                         sharex=True, sharey=True)
cols = [1, 2, 3]
rows = ['A', 'B', 'C']
for c, ax in zip(cols, axes[0]):
    ax.set_title(c)
for r, ax in zip(rows, axes[:, -1]):
    ax2 = ax.twinx()
    ax2.set_ylabel(r)
    ax2.set_yticks([])