Experimental high-pressure phase equilibrium data (cloud point and coexistence data) are reported for solutions of commercial poly(ethylene-co-vinyl acetate) samples in supercritical ethylene and ethylene-vinyl acetate (VA) mixtures, These data are correlated with an equation of state rooted in statistical associating fluid theory (SAFT). SAFT captures the effects of polymer MW, incorporated VA%, and free VA on the cloud point pressure, and on the size of the fluid-liquid miscibility gap, over a broad range of temperatures (50-250 degrees C) and polymer concentrations. Free VA is found to behave as a cosolvent (lowering the cloud point pressure), except at low temperatures (< 100 degrees C) and with low VA-containing copolymers, in which case free VA, if present in large excess (> 70 wt.%), behaves as a polar antisolvent due to favorable self-interactions among the free VA molecules, SAFT predicts a shift in the phase transition type, from upper-critical-solution-temperature (UCST), to upper-lower-critical-solution-temperature (U-LCST) with increasing flee VA in the monomer mixture.