constructed to avoid singularities, unphysical property predictions, and convergence problems when solving for the dipoles (Fig. and) due to particles with overlapping optical cores (r ij < 2a). Overlaps can naturally occur in large configurations of simulated assemblies due to coarse-grained model nanoparticle interactions, but this scattering matrix is readily inverted to obtain well-behaved solutions of eq 1 for any spatial arrangement of the particles. Similar regularization strategies have been applied to treat overlaps while simulating other physical phenomena, e.g., many-bodied hydrodynamic and magnetic interparticle forces in colloidal suspensions, which require assigning sharp particle interfaces (for continuum property modeling) together with soft-particle interactions (for dynamics). For triply-periodic geometries, M ij can be expressed in a compact form (eq S3) amenable to a highly efficient, spectrally accu-rate Ewald summation method 39 that allows the linear system for dipoles to be solved efficiently using the generalized minimal residual method (GMRES). Our implementation of MPM is publicly available (see Methods). To demonstrate the utility of MPM for design of compositionally complex nanoparticle assemblies we analyze the collective optical response of mixed nanocrystal superlattices, where the mixing ratio allows continuous tuning of effective properties. Tin-doped indium oxide (ITO) nanocrystals have a near-ideal metallic dielectric function with a tunable LSPR depending on the chosen dopant concentration (% Sn). Consistent with previous reports of other nanocrystal compositions, we found that ITO nanocrystals with different % Sn readily form intermixed two-dimensional hexagonal superlattices, as long as their sizes are closely matched (here, a ≈ 15 nm, Fig. and).