statistical mechanics - Deriving the entropy of mixing of a non-ideal solution

In the earlier posted question named Derive expression for internal energy of mixing and entropy of mixing using statistical thermodynamics the entropy of mixing was found by assuming an ideal solution. The user Porphyrin mentioned that in case the molecules in the solution do interact with each other, the free energy would have an additional term (n1+n2)x1x2w, with

w≈(2E12−E11−E22) and E12E12 is the interaction energy between molecules of type 11 and 22 when they are adjacent and similarly for E11E11 and E22E22 all of which are negative. From a consideration of the energies involved ww is expected to be positive.

My question is: how do we go about finding an answer for the entropy of mixing when we do not assume that the solution is ideal?