Me and some friends were thinking a bit about Homestuck and wondered, since both the alpha and beta timelines have their own Becquerel, and in the beta timeline there's also Jack, and also Peregrine Mendicant; is there 4 of Bec-ish characters throughout Homestuck?

No, nothing was prototyped pre-entry in the alpha session, so if someone were to wear the ring they would gain no powers except the ability to turn invisible. 

~Mod T