Imagine two 2D spacetimes, one with $x,y$ axes and the other with $x,z$ axes. They share a dimension in common with the x axis. Is it possible that a spacetime which shares at least one dimension with our four $(x,y,z,t)$ dimensions and may have other dimensions not in common with our 4 dimensions exists? In other words,can other hypothetical spacetimes have dimensions which are represented by axes such as $(x,z), (x,y,w), (y,z,t,w)$? [The $w$ denotes the 4th spatial dimension] I know the axes representing a space is arbitrary, but what I mean here is that taking our spacetime as $(x,y,z,t)$ can there be a spacetime which shares some of our dimensions and have others that we don't have?
(This is my first question asked here,so I'm not sure if this type of question is appropriate here)