Plastic pollution has become a significant environmental issue, primarily due to the increased use of single-use plastics. Multilayered plastics, commonly used for packaging, combine various polymers into complex layered structures to improve functionality and better properties. However, this intricate structure of these multilayered plastics makes recycling of them challenging. One approach for selectively recovering individual polymer components involves using compatible solvents and antisolvents. To effectively recover individual polymer constituents while minimizing solvent use and polymer degradation, understanding the phase behavior of polymer-solvent mixtures is essential. In this study, we examine the solution behavior of ethylene vinyl alcohol (EVOH) copolymers found in multilayered packaging plastics by characterizing their cloud points in dimethyl sulfoxide (DMSO) solutions under both isobaric varied temperature and isothermal varied pressure conditions. Three different commercial grades of EVOH are investigated, distinguished by their varying ethylene contents of 27 mol%, 32 mol%, and 48 mol%. The copolymer cloud points shift to higher temperatures and pressures for EVOH grades with increasing ethylene content. We also studied the changes in the solvent-antisolvent effects on the dissolution of EVOH and the corresponding cloud points of these polymer-solvent-antisolvent mixtures to optimize solvent use. A working phase diagram was constructed based on the cloud point data, illustrating the meta-miscibility zone for EVOH processability from a recovery perspective. Such working phase diagrams aid in selecting and optimizing thermodynamic parameters for selective polymer recycling technologies, specifically for recovering EVOH from multilayer plastics, thereby enhancing efficiency and sustainability in polymer recycling and reprocessing.