We develop a multiscale coarse-grain model of the NIST Monoclonal Antibody Reference Material 8671 (NISTmAb) to enable systematic computational investigations of high-concentration physical instabilities such as phase separation, clustering, and aggregation. Our multiscale coarse-graining strategy captures atomic-resolution interactions with a computational approach that is orders of magnitude more efficient than atomistic models, assuming the biomolecule can be decomposed into one or more rigid bodies with known, fixed structures. This method reduces interactions between tens of thousands of atoms to a single anisotropic interaction site. The anisotropic interaction between unique pairs of rigid bodies is precomputed over a discrete set of relative orientations and stored, allowing interactions between arbitrarily oriented rigid bodies to be interpolated from the precomputed table during coarse-grained Monte Carlo simulations. We present this approach for lysozyme and lactoferrin as a single rigid body and for the NISTmAb as three rigid bodies bound by a flexible hinge with an implicit solvent model. This coarse-graining strategy predicts experimentally measured radius of gyration and second osmotic virial coefficient data, enabling routine Monte Carlo simulation of medically relevant concentrations of interacting proteins while retaining atomistic detail. All methodologies used in this work are available in the open-source software Free Energy and Advanced Sampling Simulation Toolkit.