So-called "weak" protein-protein interactions are important for the control of solution properties and stability at elevated protein concentrations (c(2)) but are not practical to capture in atomistic simulations. This report a focuses on a series of coarse-grained models for predicting second osmotic virial coefficients (B-22) and high-concentration Rayleigh scattering (osmotic compressibility) as a function of c(2) for monoclonal antibodies (MAbs) that are of interest in biotechnology. B-22 and molecular volume along with c(2)-dependent osmotic compressibility were calculated for a series of models with increasing structural detail. Models were refined to include contributions from sterics, short-ranged van der Waals and hydrophobic attractions, screened electrostatics, and the flexibility of the mAb hinge region. The results highlight shortcomings for spherical models of MAbs and a useful balance between numerical accuracy and computational burden offered by models based on 6 or 12 spherical, partly overlapping domains. The results provide bounds for realistic values of effective charges on variable domains in order for MAbs to be stable in solution and more generally illustrate semiquantitative bounds for the space of model parameters that can reproduce experimental behavior and provide a basis for future development of computationally efficient and accurate CG mAb models to predict both low-and high-c(2) behavior.