The Universe may be only one of Many - or one of an infinity of them

Brian Randolph Greene[1] (born February 9, 1963) is an American theoretical physicist, mathematician, and string theorist. He has been a professor at Columbia University since 1996 and chairman of the World Science Festivalsince co-founding it in 2008. Greene has worked on mirror symmetry, relating two different Calabi–Yau manifolds(concretely, relating the conifold to one of its orbifolds). He also described the flop transition, a mild form of topology change, showing that topology in string theory can change at the conifold point.

Here is a link to a talk by him about the universe - or rather the multiverse.

I like this idea.  It seems plausible.

My question: Does String Theory allow the number of universes to correspond to the number of positive integers or the number of real numbers between 0 and 1, or an even greater number?