How can I run 3 4K monitors on my 2015 MBP
The way you connect more than 2 external displays to a MacBook (or any laptop for that matter) is to use USB display adapters like the StarTech USB 3.0 to 4K DisplayPort External Multi Monitor Video Graphics Adapter



Each one of these adapters will function like a separate graphics card allowing you to hook up as many monitors as you have adapters.  So, to get your six external monitors, you can have two natively connected to your MacBook Pro and then you will need 4 of these adapters. 

*Note:  It's important to note that this setup is not for gaming.  These are not high performance external GPUs.  This is for connecting an additional display.  

Additionally, there are limitation with with OS X that will cause performance problems.  Some are limitations due to Apple, and others are limitations due to the driver.  Always check the Release Notes prior to purchase and/or installation.

If you're on a 2013 or later Mac Pro, you can natively connect 3 monitors without the need for special adapters.  However, there is a caveat with the Thunderbolt 0 bus and HDMI port.  

See How do I connect a 3rd 4K monitor to my 2013 Mac Pro?