Dimensional shift

Leaving aside the question of whether the universe contains ten or eleven dimensions, as in string theory, or many mansions of indeterminate number, as in the New Testament, let us suppose that this multiverse, or set of all possible universes, consists of n dimensions, so we feel absolutely unconstrained about what is possible. Also let us suppose there is no particular decorum about whether, in shifting from one dimension to another, we have to go through them in order. So if you want to go from the third to the fifth dimension, you do not have to go through the fourth in the usual manner. This would be possible if there were an interdimensional henadic cosmitorium, a manifold hall of portals, each one of which leads to a different non-prexisting spontaneously manifesting surprise. A Schrodinger cat in every garage?