I think I can answer this in more laymen's terms. In relativity theory, space and time are very closely related. For example, when you pass by me, I measure that your wristwatch runs slower than mine, and I measure that you are shorter in your direction of motion than you would be if you stopped to talk to me. Even at walking speed this is true, if only undetectably. From your perspective your wristwatch always runs at its normal rate, and your length in your direction of motion isn't affected by your motion relative to me.
In relativity theory an observed distortion of time always goes hand-in-hand with an observed distortion of space (length), and by the exact same percentage, so it became convenient to consider that those two concepts are two sides of a coin, so to speak, hence the term spacetime. It also became convenient to think of observed objects and events in terms of 4 dimensions, the 3 of space and one of time.
Of course that's a rough way to put it, but I think it's not much more involved than that. So no, the theory doesn't support more than one time dimension.