Given any two models, can you always find a meta-model that includes them both?

I think this is a confused question. The answer is yes, but when I tell you what the meta-model is, I don't think your underlying curiosity will be satisfied.

Given 2 models A and B, we can construct a model C. The set of objects in C will be the union of the set of elements of the form (A, a) for all objects a in the model A, and the set of elements of the form (B, b) for all objects b in the model B. Then every proposition about A can can correspond to a proposition about C, particularly about its objects of the form (A, a), by simple substitution of (A, a) for a; and similarly propositions about B correspond to propositions about the objects of the form (B, b). This is, of course, a trivial combination in which the parts that correspond to the original models do not interact with each other at all, hence my belief that you will not be satisfied.

Perhaps a better question to ask would be: is there a meta framework that distinguishes some mathematical systems as "good" and others as "bad"? I think the answer to this question is the criteria that a mathematical system be self-consistent, that is, it does not produce contradictions. Of course, this criteria is not always possible to verify.