In a phase envelope, an adequate description of the critical point is of high importance. It identifies the conditions where the bubble and dew curves meet, and where the nature of the single phase region outside the phase envelope changes. The knowledge of the mixture critical point is relevant to preventing production and transport problems, as well as to optimizing near-critical and supercritical processes. A modified cubic plus association (CPA) model was recently shown to accurately describe the vapor-liquid equilibrium (VLE) critical temperatures and pressures of pure compounds. The model is usually fitted to pure component data between 0.45T(r) and 0.85T(r), while forcing the correct description of both T-c and P-c. Here, the performance of the model is evaluated for mixtures. Interaction parameters are regressed from VLE/liquid-liquid equilibrium (LLE) data at lower temperatures. Accurate results, for binary and ternary mixtures, were obtained. These results concern mainly mixtures containing, water, alkanes, alkanols, and amines. The results obtained are compared to those from perturbed-chain statistical associating fluid theory (PC-SAFT), simplified CPA (s-CPA), and Soave-Redlich-Kwong. Results for liquid-liquid critical temperatures are also analyzed for mixtures of methanol/ethanol with alkanes. The average absolute deviations with this approach, when considering VLE fitted binary interaction parameters, are 0.58 for T-c and 5.18 for P-c for the VL critical point (CP) data in analysis. For LL CP, the model can describe the results for compounds, with similar critical properties, as is the case of methanol and hexane.