The proposed mixing rule can be formally interpreted as an approach considering the triple cohesive interactions of a part of the molecules in a mixture as follows: a = k Sigma(2)(i=1)Sigma(2)(j=1)x(i)x(j)a(ij)(1 - k(ij)(T)) + (1 -kappa)Sigma(2)(i=1)Sigma(2)(j=1)Sigma(2)(k=1)x(i)x(j)x(k)a(ijk), where k(ij)(T) and K are the system-dependent adjustable parameters. Regardless of its possible theoretical justification, the proposed mixing rule is equivalent to the classical mixing rule with the composition-dependent adjustable parameter k(ij)(T), and this dependence follows the regularities typically required for an accurate modeling of experimental data. This study demonstrates that the proposed mixing rule allows an accurate description of the entire thermodynamic phase space involving liquid-liquid-vapor equilibria, vapor-liquid equilibria, and the high pressure liquid liquid equilibria. However in some complex cases it still may not cancel a need of evaluating the binary parameter l(12).