Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to the Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model developed based on the AMOEBA+ framework captures various liquid phase properties in molecular dynamics simulations while remains consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.