Can the 2016 15-inch MacBook Pro (with Touch Bar) drive 4 external monitors?
The 2016 15" MacBook Pro will support up to four external displays.

You can have either of the following two options:


Up to two 5K displays
Up to four 4K displays


Specifically per the tech specs of the 2016 MacBook Pro:


  Simultaneously supports full native resolution on the built-in display
  at millions of colors and:
  
  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 over a billion colors Thunderbolt 3 digital video output
  
  Native DisplayPort output over USB‑C VGA, HDMI, and Thunderbolt 2
  output supported using adapters (sold separately)


The 13" model will support up to 2 external displays either


One 5K display
Up to two 4K displays