[aephi alum]

Something like that happened at my school, with a fraternity. A fraternity went through a reorganization, and only a handful of brothers were invited to remain as actives; the others became alums. The "alum" brothers formed their own local fraternity. A few years later, that local became a colony of a different national.

I don't see why the situation you describe couldn't happen. If all sisters from the PSS days had graduated, no problem. If there were still actives around who'd been initiated into PSS, they could not be initiated into XO as well... either they'd go alum or XO would wait until they'd graduated. If XO offered alum initiation to alums of TGZ, of course, those who had been initated into PSS could not accept.