Generally the idea of a crossover game is to play around with a setting or character you like. Kamen Rider is a pretty common one, for example. Having people play original characters that are tied to a preexisting setting forces them to be somewhat more creative than just picking Saber or whoever, while also keeping things grounded in a given setting on some level so you don't have cyborg vampire wizard demigods running around. I mean, barring someone bringing in a setting that actually has cyborg vampire wizard demigods.

Joining up just to have your super special character from your super special original universe travel across planes of existence and punch random people in the face kind of feels like missing the point but I guess that might just be me.

Anyway, expressing interest.