We have recently developed a compressible lattice model for representation of both low-pressure and high-pressure phase equilibria in CO2 + polymer systems. The model explicitly accounts for weak complex formation in these systems, using two parameters that are obtained by fitting experimental cloud point pressures or sorption equilibria. Furthermore, we have shown that these parameters can be obtained from spectroscopic measurements, or molecular dynamic simulations. In the present work, we extend the model to CO2 + cosolvent + polymer systems, using parameters obtained from cloud point data in the binary systems. Applications of the model to the study cosolvent effects of acetone, dimethyl ether, and chlorodifluoromethane in CO2 + poly (caprolactone) and poly (lactic acid) systems are described, combined with experiments using FTIR spectroscopy. Finally, we demonstrate that the model can also predict solubilities of multicomponent gases in polymers membranes.