van der Waals (VDW) dispersion forces are often calculated between colloidal particles by combining the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory with the Derjaguin approximation; however, several limitations prevent using this method for nanocolloids. Here we use the Axilrod-Teller-Muto 3-body formulation to predict VDW forces between spherical, cubic, and core-shell nanoparticles in a vacuum. Results suggest heuristics for "designing" nanocolloids to have improved stability.