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Cross-association between molecules may result in several conformations of weakly bound molecular complexes with different association energies. However, the conventional combining rules used in equations of state account only for one conformation. Therefore, in the present work we introduce a framework that allows one to distinguish the cross-interactions between sites of different nature and to expand the number of captured conformations coexisting in the mixture. We incorporated the proposed approach into the Cubic-Plus-Association (CPA) equation of state and applied it to model the binary Vapor-Liquid Equilibrium (VLE) of aqueous mixtures with alcohols (methanol, ethanol, propan-2-ol, tert-butanol, and phenol), acetic acid, and CO2. For the mixtures with alcohols, we report the quantum chemical association energies calculated with the benchmark Domain-Based Local Pair Natural Orbital Coupled-Cluster Single, Double, and Perturbative Triple DLPNO-CCSD(T) approach and compare these values with association energies obtained by fitting to experimental data using a distinguishable interactions approach. Based on the updated results for the binary systems, we investigated how the new cross-association parameters will affect the predictions of the ternary Liquid-Liquid Equilibrium (LLE) of water–alcohol–hydrocarbon mixtures and VLE of water–acetic acid–CO2 mixtures.