The description of each separable contribution of the intermolecular interaction is a useful approach to develop polarizable force fields (polFF). The Gaussian Electrostatic Model (GEM) is based on this approach, coupled with the use of density fitting techniques. In this work, we present the implementation and testing of two improvements of GEM: the Coulomb and Exchange-Repulsion energies are now computed with separate frozen molecular densities, and a new dispersion formulation inspired by the SIBFA polFF, which has been implemented to describe the dispersion and charge–transfer interactions. Thanks to the combination of GEM characteristics and these new features, we demonstrate a better agreement of the computed structural and condensed properties for water with experimental results, as well as binding energies in the gas phase with the ab initio reference compared with the previous GEM* potential. This work provides further improvements to GEM and the items that remain to be improved, and the importance of the accurate reproduction for each separate contribution.