MacBook Pro Display – MacBook Pro Support for 3840 x 1600 and Higher Resolutions

I'm going to start off backwards. 4k Display will require some sort of cable, wether DVI, Display port, or Thunderbolt that is from manufacturer to manufacturer and model to model different. According to the tech specs of 4K it is compatible with Display port 1.2.

According to : http://www.apple.com/macbook-pro/specs-retina/

"Dual display and video mirroring: Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on up to two external displays, both at millions of colors"

This could however simply be that Apple has only tested it on displays with that resolution and once 4k displays are out in the real world people can test it.

So your MBP Retina can support 2 external displays and the use of the the clamshell display at the same time. Those external display can be attached via HDMI and Thunderbolt (adapters) or both via Thunderbolt adapters. But so far the tech specs limit the resolution to 2560x1600. It could also be that the resolution output could be enhanced with a software update (firmware update) at a later time.

Archived Specifications page:

• MacBook Pro (Retina, 15-inch, Late 2013) - Technical Specifications
• Other MacBook Pro models.

You are outside "supported" territory with using three screens on that hardware.

• https://support.apple.com/en-us/HT204154 - thunderbolt FAQ
• https://support.apple.com/en-us/HT206587 4k and 5k and beyond

That being said, you can try connecting things and Apple hardware is known to run more displays than the "support" document allows. Usually it's due to driver updates that can still juggle all the connections but that the performance isn't there or you end up with glitches like frozen screens or just not the frame rates Apple likes to see on supported hardware combination.