The recently introduced modification of the Lee-Kesler-Plöcker equation of state, LKP-SJT, has been further developed, and the results are presented. The new version includes an enhancement of the original approach for calculating the compressibility factor at the critical point. Furthermore, the standard fluid combination used as base points for interpolation has been varied. The results of these calculations are compared with datasets generated from highly accurate equations of state in terms of the Helmholtz energy and with experimental measurements. The investigated fluids include alkanes and carbon dioxide. In comparison to the original version of the LKP-SJT equation of state, improvements were achieved for n-alkanes up to n-dodecane and carbon dioxide. The calculated densities of long-chain alkanes are significantly more accurate, while vapor pressures are less precise. The application of the LKP-SJT to propane - n-alkane and carbon dioxide - n-alkane mixtures up to n-decane confirms its benefits in the density calculation of long-chained alkanes and hence asymmetric mixtures. Calculations of the liquid density for the propane - n-eicosane mixture performed to estimate the extrapolation behavior yield promising results.