I know string theory suggests there might be 11 dimensions that are tightly wrapped into an extremely small space. What I'm wondering is whether there could be a dimension extending outward beyond the three we're familiar with. My favorite science book is Flatland which explores this, but in the light of modern discoveries and current theories, is it still considered possible? Is there anything that prohibits it?

It seems to me that an expanded fourth dimension could play a roll in quantum entanglement, although I'm sure someone must have considered this before.