I will link you to some work that has been done on this idea from data from WMAP, Planck and other satellites, and the analysis therein experimentally and theoretically.
arXiv articles (highly technical):
"First Observational Tests of Eternal Inflation"
"Eternal inflation and its implications"
"First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results"
I'm not sure what level of inquiry would be accessible to you, but there is also a presentation with pictures that Feeney gave on a lecture tour I believe that may be more understandable if you don't have any undergraduate degree in Physics. (you may have to just skip all the math if you are unfamiliar with it).
In short, yet it is possible that there are "other" universes, normally formalized as manifolds endowed with a lorentzian metric. It is not a necessary condition that other universes have the same number of dimensions, or any other broad overarching properties such as the geometry of the universe. Experimentally, it turns out that our universe is very close to euclidean (meaning completely flat, a triangle inscribed in our manifold will have angles that add up to near 180 degrees). It could be that there are other universes with hyperbolic geometries, or even stranger geometries!
My personal opinion, which relies heavily on the philosophical position of ontological maximalism is that geometric topology underlies the "set of all universes" in the multiverse. I think that there is a general category of objects that can be investigated by geometric topology that describes every possible geometry that a universe can have, and that currently in the multiverse each of these objects is existing, although they may be under some type of homeomorphism. But, my personal opinion is extremely far out there, I'm fairly sure no one believes that. If you are interested in some introductory stuff on what I mentioned in the last paragraph you may want to check out this easily accessible article of geometric objects in different dimensions: http://plus.maths.org/content/richard-elwes