The issue is that we only observe one dimension of time and three dimensions of space. So allowing more than that would require a lot of evidence.
Postulating that there's multiple times dimensions is the same thing as postulating that there's more than three space dimensions in string theory. You make the maths "easier" by postulating that there's more dimensions, but you don't make any predictions that the 3+1 spacetime theory doesn't make and that can be observed experimentally.
Postulating that there's multiple times dimensions is the same thing as postulating that there's more than three space dimensions in string theory. You make the maths "easier" by postulating that there's more dimensions, but you don't make any predictions that the 3+1 spacetime theory doesn't make and that can be observed experimentally.