Someone can correct me...but, I'll contribute.
Strictly speaking, any 4 player game isn't "JAMMA". Much the same way any game with more than 4 buttons (I beileve 3 is the common number, but JAMMA will support 4) isn't "JAMMA" it'd be a "JAMMA+" deal.
And with any JAMMA+ you'll have an extra connector on the game PCB (a 'kick harness' since it was usually used for the kick buttons in Street Fighter). You'd...if I'm not mistaken... you'd have to wire up your extra controllers and buttons via this spot on the board.
I own no 4 player games, I've never set one up (acutally I do own a 4 player game...I just never had a cab for it) so I'm just going by what my understanding is.
In a nutshell, you'd have to have a connector specifically made for that board that will let you run the extra controllers in.