Does the MacBook Pro retina display (late 2013) have support for displays with 3840 x 1600 (WQHD+) (LG example shown below).
If so, at what refresh rate and through what port?
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Using these three sites: Apple display site, Apple Insider site, and MBPr site, I have what I believe to be the correct answer. Using HDMI, you should be able to use a WQHD+ screen at 30Hz. Apple Insider's site recommends the LG 34UM88-P. Unfortunately, it doesn't appear that you computer supports 4K at anything higher than 30Hz. Please let me know if any of the information stated is incorrect. I would recommend finding a store that stocks the monitor you are looking to buy, and asking them if you can bring in your laptop and an HDMI cord to test the monitor and make sure it is compatible with your computer.
You can use even higher 4k resolution (different monitor) via DisplayPort. You can even connect two monitors, 60Hz.
Check Amazon Q&A for similar or higher monitors:
You can actually run 2 of these at full 3840x2160 at 60Hz on a late 2013 15" MacBook Pro with Retina! You can't daisychain them, but if both of your display ports are free, you can connect 2 of them and they look amazing!
Macbook Pro late 2013 Retina (15 inches) can run at 3841x2160 with help of third-party utilities.
And NVIDIA GeForce GT 750M 2048 MB official site provides even higher specs.