This paper describes the application of the modified additivity rule (MAR) to the calculation of total (counting) electron-impact ionization cross sections of complex molecules with sum formulas of the form A(x)B(y), A(x)B(y)C(z), and A(p)B(s)C(t)D(u). The MAR incorporates weighting factors for the contributions to the molecular ionization cross section from the ionization cross sections of the constituent atoms, which depend explicitly on the atomic radii and the effective number of atomic electrons except for a few special cases (hydrides where the other constituent atom has a radius smaller than the radius of the H atom and species where both constituent atoms have radii smaller than the radius of the H atom), where the weighting factors depend only on the atomic radii, i.e., on geometric effects. A comprehensive comparison of the predictions of the modified additivity rule with available experimental data and with other theoretical predictions is presented.