Greg Egan has written a series called Orthogonal which explores a universe that contains different rules for the time dimension than ours.
In Orthogonal the metric signature explored is (+,+,+,+).
In Dicronauts the metric signature explored is (-,-,+,+).
(We live in a universe with metric signature (-,+,+,+).)
As a matter of fact, many physicists work with a signature of (+,-,-,-) to describe the spacetime of our universe.