We can see in three spatial dimensions (length, width, and height). Some consider time a 4th dimension, but it is hard to concieve of it being a spatial one.
We "know" only of those three/four, although we have "theorized" many, from 5 to hundreds, depending on the cosmological theory.
Then there's the "Many Worlds" theory, popular in some Science Fiction, that supposes that every decision or possibility spins off an alternate "timeline" where those events happened in every possible fashion. And since possibiulities are infinite, the numbers of possible dimensions would then also be infinite, and constantly increasing.
For example, there could be a universe where I didn't answer this question, or did, but simply didn't answer this addendum. Or left in the typo I just changed. et cetera ad nauseum.