In model theory for *standard* first-order logic, one constructs a single model, a reduced product, from a collection of first-order models, together with an index set and a filter on the index set.

In model theory for *modal* first-order logic using Kripke frames, one constructs a single model containing substructures ("possible worlds") that are similar to individual classical models.

It appears to me that for certain systems of modal logic such as S5 and perhaps S4, one might construct modal models as reduced products of classical models. One would need to make an appropriate choice of a filter on the index set, and also of a topology on the index set, so that the modal operators might be mapped to the corresponding topological operations.

I have not located any research along these lines. I would be interested to hear about anything that has been done, or from anyone who might be interested in pursuing this topic.