Well,
Mach3 in essence can handle up to 6 axis, so if that is all it has then certainly it can work. Besides you could operate a modbus plc to free some axis work from mach (toolchanger etc..)
BEing a punch, plasma and plate marker in one, make it a hard retrofit, but certainly doable.
Not for beginners though.
Maybe if you post more info on the machine
Motor types, driver types, does it have a toolchanger, how about a torch height control?
Another thing to consider is how would you generate G-code for them... plasma is no problem, dont know about the punch and plate marker.
Best regards
Fernando