In this work, we explore the capabilities of the statistical associating fluid theory for potentials of the Mie form with parameter estimation based on a group-contribution approach, SAFT-γ-Mie, to model the phase behavior of the (carbon dioxide + n-heptane + methylbenzene) system. In SAFT-γ-Mie, complex molecules are represented by fused segments representing the functional groups from which the molecule may be assembled. All interactions between groups, both like and unlike, were determined from experimental data on pure substances and binary mixtures involving CO2. A high-pressure high-temperature variable-volume view cell was used to measure the vapor-liquid phase behavior of ternary mixtures containing carbon dioxide, n-heptane, and methylbenzene over the temperature range 298-423 K at pressures up to 16 MPa. In these experiments, the mole ratio between n-heptane and methylbenzene in the ternary system was fixed at a series of specified values, and the bubble-curve and part of the dew-curve was measured under carbon dioxide addition along four isotherms.