We recently proposed the dipole-quadrupole (DQ) method for transforming adiabatic electronic states to diabatic states by using matrix elements of the dipole and quadrupole operators, and we applied the method to 3-state diabatizations of LiH and phenol. Here we extend the method to also include the electrostatic potential, and we call the resulting method the DQΦ method, which denotes the dipole-quadrupole-electrostatic-potential diabatization method. The electrostatic potential provides extra flexibility, and the goal of the present work is to test and illustrate the robustness of the methods for producing diabatic potential energy curves that tend to the adiabatic curves away from crossings and avoided crossings and are smooth in regions of crossings and avoided crossings. We illustrate the generality of the methods by an application to LiH with four states and by two-state diabatizations of HCl, (H2)2, O3, and the reaction Li + HF → LiF + H. We find that - if enough states are included - the DQ method does not have a significant dependence on the parameter weighting the quadrupole moment, and a geometry-independent value of 10 a0 -2 is adequate in all cases tested. We also find that the addition of the electrostatic potential improves the diabatic potentials in some cases and provides an additional property useful for increasing the generality of the method for diabatization.