This question already has an answer here:
There are a number of models (String theory, Cascading Gravity, Emergent Dimensions) that contain extra space like dimensions. Why do people tend to avoid considering extra timelike dimensions?
The only reason I have heard so far is that you want to avoid close timelike curves (which would violate causality). I would think that if causality is respected in our usual time dimension, we could (at least for the purpose of initial toy models) demand causality be respected in other time dimensions as well.
(The m+n dimensional question linked to was asking about what happens if m and n are be integers.)