oh i think i got confused with the touch input detection, i think touch should work for custom buttons(but im not entirely certain i remember that has a detect input at index 0,1,2,3,4,5,6 etc which detects the buttons on mouse or multi touch screen but again not sure if applies to mouse or only to touch), but yea, multiple mouse buttons should be supported, nice request +1.
however i have a gaming mouse, but the extra side buttons, are by default for browser forward/backwards, unless i map them in the mouse settings in windows. so you see that games made in C2 if are not exported in NW.js or for desktop platforms, wold have a issue even if mouse multiple buttons are supported. since wold switch the browser... but i guess it could be made so it overrides the default functions if supported as C2 plugin. but im not sure how practical that wold be. im guessing the best approach wold be to create the mapping of the gaming mouse by Browser.object to cancel the gaming mouse default controls for the extra buttons, and assign them to something else in the game in a menu but that is an entire headache, by itself.
Edit2: maybe this request should be in the Plugin request section? maybe some plugin guru will pick up the challenge?