Fedora 20; Python 2.7.5; Matplotlib 1.4.3 (installed by yum/pip)

I need to visualize some complex multivariate datasets and the preferred way is to use a modification of parallel axis visualization, using stacked 2D plots, where each plot maps a degree of freedom/model parameter and data points belonging to the same data sets should be interconnected across different plots. I am attaching a conceptual sketch. How could I implement it in matplotlib?

I put emphasis that each plane should be a plot itself with its own axes with their own scales. More specifically, all plots have the same x-axis, but the y-axis represents something different.