Is it possible to connect 3 non-Apple monitors to a 2014 macbook pro retina without adding extra hardware
It doesn't matter if you have the 13 inch or the 15 inch model - Apple supports two external monitors. One HDMP or Thunderbolt. The other Thunderbolt.

You'll need extra hardware to connect more displays or even ones that don't connect to the ports on the hardware.

See footnote 4 in https://support.apple.com/en-us/HT204154


  MacBook Pro (Retina, Mid 2012), MacBook Pro (Retina, 13-inch, Late 2012), and Mac Mini (Late 2012 and later) computers can use an HDMI-compatible device on it's HDMI port while using one Thunderbolt display, or they can use two Thunderbolt displays.