I doubt it. That would mean Izuki now has several powers aside from All Might's super speed and strength, unless all that came before him are quirkless, a detail that would've been mentioned when All Might spoke about himself being quirkless.

Also, All Might never showed different quirks even in desperate battles, so I think One for All is just incredibly enhanced physical abilities. I also think the latent power of the transferable quirk was already very high from the start.