Experimental cloud-point data to 250 degrees C and 2000 bar are presented to demonstrate the impact of dimethyl ether (DME) and ethanol on the phase behavior of poly(ethylene-co-acrylic acid) (3.9 mol % acrylic acid) (EAA(3.9))-butane mixtures. The addition of 6.4 wt % DME to the EAA-butane system decreases the cloud-point pressure from 2000 to 650 bar at 165 degrees C due to the cross-association of dimethyl ether and acrylic acid in EAA(3.9). At high DME concentrations, its impact is reduced as the amount of DME increases since polar interactions between excess DME increase after the acrylic acid sites are saturated with DME. Ethanol is a better cosolvent than DME at low ethanol concentrations. The addition of 2.2 wt % ethanol decreases the cloud-point pressure from 2000 to 650 bar at 165 degrees C due to the cross-association of ethanol and acrylic acid in EAA(3.9). Ethanol becomes an "antisolvent" at concentrations greater than 16 wt % as excess ethanol self-associates, forming multimers that increase the polarity of the mixture. The cloud-point data are modeled with statistical associating fluid theory (SAFT). The ternary calculations use temperature-independent, binary mixture parameters whose values are obtained by fitting the phase behavior of the three binary pairs that form the ternary system. SAFT correctly predicts the trends observed in the cloud-point curves from zero to 100 wt % DME, although quantitatively it overestimates the effect of DME. SAFT underestimates the effect of ethanol, as the calculated one-phase region is smaller than that observed. However, SAFT correctly predicts the decreasing impact of ethanol with increasing ethanol concentration and that ethanol becomes an antisolvent at high ethanol concentrations.