The liquid-liquid equilibrium (LLE) phase boundaries were determined experimentally for the ternary systems containing refined sunflower oil, methanol, and one of ten potential cosolvents at 308.2 K under atmospheric pressure by using cloud point method. n-Butylamine was found to be one of the best cosolvents, which could substantially enhance the miscibility between the oil and methanol. The LLE measurements were then extended to the ternary systems of methanol + refined sunflower oil, soybean oil, or canola oil in the presence of the auxiliary cosolvent n-butylamine at temperatures from 298.2 K to 318.2 K. The LLE data were utilized for estimating the model parameters of the NRTL and the UNIQUAC, respectively. In general, these two models can reasonably represent the LLE phase boundaries.