Can Mid 2015 Macbook Pro Run 3 External Monitors?
YES.  It can be done if your MBP has the extra graphics chip AND you use Displayport as one of the monitor inputs.  Click on "About this Mac"  "System Report" "Graphics/Displays" and look to see if it has 2 graphics chips one of them being "AMD Radeon R9 M370X"

My experimentation has taught me this:


2012 MBPR with extra graphics chip can drive 2x TB-DVI + 1x HDMI
2015 MBPR with single integrated graphics can only drive 2x of any combination as poster indicates (it cannot drive the combination in #3 below)
2015 MBPR with extra graphics chip can NOT drive 2x TB-DVI + 1X HDMI but it CAN drive 1x TB-DVI + 1x TB-DisplayPort + 1x HDMI as one of the answers here indicates.


I don't know what changed between 2012+extra graphics and 2015+extra graphics to require that one of the displays be using displayport input (vs DVI/HDMI/VGA).  Wish there was a way as I now need to get another monitor...