Can the current model MacBook Pro (2017) 15" power 3 Displays from one port? I know the Apple site says this regarding the number of displays:


Up to two displays with 5120-by-2880 resolution at 60Hz at over a billion colors
Up to four displays with 4096-by-2304 resolution at 60Hz at millions of colors
Up to four displays with 3840-by-2160 resolution at 60Hz at over a billion colors


But I'm trying to find the cleanest solution for connecting this thing to 3 monitors without having a bunch of wires connected. I also know very little about the power restrictions and the connectivity of how the Thunderbolt ports are setup. Are they effectively on the same bus? Is connecting to one the same as connecting to all? Are they (hardware-wise) divided between the two sides they're on?

I'm also unable to find any docks that support 3 displays, only 2.

Ideally, I'd like to be able to plug in a single dock, and have that dock power 3 displays. I'd like to know if it's possible, and if so, what dock there is. If it's not possible, will just using two docks on the same side of the machine be okay?
It's a matter of available bandwidth of the Thunderbolt port, not the dock itself.

A Thunderbolt 3 port has enough display bandwidth to handle a single 5K @60H display or two 4K displays at 60HZ.  

On the 15" MacBook Pro (2017), it has two Thunderbolt controllers, so you can now attach a second 5K display or two more 4K displays.  But because it's on a second controller, it will have to be on a different port.

From Apple's Thunderbolt Page


  Thunderbolt 3 provides twice the display bandwidth of Thunderbolt 2,
  enabling iMac to support two 4K displays or one 5K display. And with
  two Thunderbolt controllers in the 15-inch MacBook Pro, you can send
  graphics to dual 5K displays for the perfect high-resolution photo and
  video editing setup.


The dock can support 2 displays, because that's the maximum that can be supported by the port.  To get a 3rd and 4th display, you would have to use a different Thunderbolt port on the MBP.

However, you could (theoretically - meaning I have never personally tested this) put a USB to DVI/DisplayPort/HDMI adapter on one of the USB ports of the dock and get a 3rd display, but I currently can't see how you would get 4K out of it.