A previous method of the author is modified in order to ensure (i) a better evaluation of the solvent activity coefficients at infinite dilution and (ii) the calculation of liquid-liquid equilibrium (LLE) for athermal solutions also. The first goal is obtained by imposing that the epsilon parameter, which corrects the entropic term of the Flory-Huggins equation as required by the previous work, varies not only according to the density of pure components but also according to the molar volume compositions. The second problem, linked to the demixing phenomena occurring at the upper and lower critical solution temperature (UCST and LCST) points for athermal solutions also, suggested a simple modification of the enthalpic term. It is assumed that the chi parameter is not nil for nonpolar mixtures also when the density of pure polymer is remarkably different from the mixture density. While the method is predictive for vapor-liquid equilibrium (VLE) and the weight fraction activity coefficients at infinite dilution, the LLE data can only be correlated by using "ad hoc" empirical parameters. Further, an empirical procedure is proposed to predict the UCST and LCST points of both polar and nonpolar mixtures which requires only the knowledge of the molecular weight of solvents and the density of polymers. A comparison is made with well-known literature methods which predict the equilibrium data for many systems in both the VLE and LLE ranges.