Could have been suggested before since I think I have seen it in forum mafia set ups.
However, I think it would be really cool to have a yakuza faction (which functions just like another mafia faction).
They would be function exactly the same yet perhaps the sheriff would get a message of "your target is a member of the yakuza!" instead of mafia.
Titles could be tweaked to be more fitting but it really wouldn't matter (i assume the yakuza doesnt have a gofather). You could also just have them be a rival mob and still just be called the mafia.
They would have a separate night chat and could not win with the other mafia group.
I think it could easily be played with a 9-3-3 setup (2nd maf group instead of neuts) or you could even go with something like 2-2-2-9 (2 pairs of maf, 2 neuts, 9 town).