The conductor-like screening model for realistic solvation (COSMO-RS) was introduced 20 years ago and meanwhile has become an important tool for the prediction of fluid phase equilibrium properties. Starting from quantum chemical information about the surface polarity of solutes and solvents, it solves the statistical thermodynamics of molecules in liquid phases by the very efficient approximation of independently pairwise interacting surfaces, which meanwhile was shown to be equivalent to Guggenheim's quasi-chemical theory. One of the basic limitations of COSMO-RS, as of any quasi-chemical model, is the neglect of neighbor information, i.e., of local correlations of surface types on the molecular surface. In this paper we present the completely novel concept of using the first-order COSMO-RS contact probabilities for the construction of local surface correlation functions. These are fed as an entropic correction for the pair interactions into a second COSMO-RS self-consistency loop, which yields new contact probabilities, enthalpies, free energies and activity coefficients recovering much of the originally lost neighbor effects. By a novel analytic correction for concentration dependent interactions, the resulting activity coefficients remain exactly Gibbs-Duhem consistent. The theory is demonstrated on the example of a lattice Monte Carlo fluid of dimerizing pseudomolecules. In this showcase the strong deviations of the lattice Monte Carlo fluid from quasi-chemical theory are almost perfectly reproduced by COSMO-RSC.