How can I make 3 external displays function with my 13-inch Retina MacBook Pro (Mid 2014)?
The 15" and 13" MacBook Pros are vastly different machines. The 15" has a dedicated video card that may help support that many displays. The 13" uses Intel's embedded video hardware, and it likely does not (at least not in OS X). As the user states in that post, it seems technically possible to run 3 in Linux, but it appears restricted in OS X.

That said, you could always find a USB-based video adapter and use it to run and additional display. It would function independently of the internal hardware.