In Rebirth will there still be just the two floor varieties? Or will a third be introduced? For example another alternate besides The Basement + The Cellar?

there wont be any new alts.. but each of the floors will be greatly expanded to the point of there basicly being more alts… the visuals are also expanded to look like there are more variations of the same chapters… so yes, and no. 

there is enough content for there to be new alts, but there are no new area names (in the early game)