A new UNIQUAC associated-solution model taking into account association of hydrogen-bonding molecules and solvation between unlike molecules with allowance for a non-polar interaction was presented to predict the ternary and quaternary liquid–liquid equilibria (LLE) for the mixtures of associating molecule acetonitrile, aniline, and methanol with non-associating components. The 17 ternary systems were represented successfully using only binary parameters. The model was further used to represent the experimental tie-line data for quaternary mixture of the methanol+2,2,4-trimethylpentane (TMP)+methyl tert-butyl ether (MTBE)+tert-amyl methyl ether (TAME) system and those of constituent three ternary mixtures of the methanol+TMP+MTBE, methanol+TMP+TAME and methanol+TMP+toluene systems measured at the temperature 298.15K and ambient pressure. Good agreement between the experimental results and those calculated by the associated-solution model was obtained. Additionally, the results were compared with those calculated by extended and modified UNIQUAC models that assume no chemical equilibria between associating molecules.