How can I make 3 external displays function with my 13-inch Retina MacBook Pro (Mid 2014)?

How can I make 3 external displays (4 total, or 3 if running in closed book mode) function with my 13-inch Retina MacBook Pro (Mid 2014)?

Regardless of closed-book/clamshell mode, I am unable to make 3 external displays function. I am able to connect it all and power any given two at a time and it obviously has enough power, but it doesn't seem to want to run 3.

I've read mixed answers as to whether it can support 2 or 3 external displays. Someone in a thread on OWC says it can and they show a 15" MBP powering 3 externals.

Is there something I'm missing or a work-around?