I have infinitely many questions about how this monstrous amalgamation of properties came to be, but I'll put those aside for the time being and remain highly intrigued.
English
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Well, I know ArcSys made Blazblue and P4 Arena. I'm not sure about Undernight though. I'm also pretty sure that the creator of RWBY was a fan of the Guilty Gear and Blazblue games.
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Honestly, three of the four have a similar enough combat setup that I can see it being doable. P4A is Arc System Works, and RWBY's style lends itself to the same. (Light, Heavy, Slash, SP) SP for each is obvious. Persona users call on their Personas, BlazBlue fighters use their Drive attack, and RWBY characters activate their semblances.