Is it possible to use maxent methods to build models for data in more complex situations?

For instance: non-constant average. Say: if I wait 6 minutes for a cab, this will take me to a part of the town where the average waiting time is larger, whereas if I wait 3 minutes, this will take me to a part of town where the average waiting time is smaller. (Might I combine maxent with mechanistic modelling, for such a scenario?)

Or: I want to model not just one random variable, but several (so I want to model joint probability for Xk random variables, each with sets of probabilities p_ik).

Or: the constraints are not available in closed-form expression.

Or other scenarios. Are there maxent-like methods for such situations, and would you have references for such methods, please?