We extend our previously developed approach for generating "physically-motivated" force fields from symmetry-adapted perturbation theory by introducing explicit terms to account for nonadditive three-body exchange and dispersion interactions, yielding transferability from the gas- to condensed-phase. These Axilrod-Teller-Muto-type three-body terms require no additional parametrization and can be implemented with high computational efficiency. We demonstrate the accuracy of our force fields for a diverse set of six organic liquids/fluids, examining a wide variety of structural, thermodynamic, and dynamic properties. We find that three-body dispersion and exchange interactions make significant contributions to the internal pressure of condensed phase systems and cannot be neglected in truly ab initio force field development. These resulting force field parameters are extremely transferable over wide ranges in temperature and pressures and across chemical systems, and should be widely applicable in condensed phase simulation.