Monoclonal antibodies are bivalent molecules and are thus able to engage two antigens concurrently, a property termed avidity. The therapeutic efficacy of an antibody drug can be broadly defined as a consequence of either antigen occupancy or target cell opsonization. Therefore, depending on the intended mechanism of action, avid engagement of a therapeutic antibody may be desirable in order to attain high antigen occupancy and consequent antagonism. In some cases, such as target cell opsonization and Fc-mediated cytotoxicity, avidity may limit efficacy when antigens are occupied with fewer antibodies per cell. In this study, we utilized a mathematical model of antibody-antigen binding to identify conditions under which avidity hinders or enhances therapeutic potential. We calibrated the model with in vitro assays exploring the binding of a bivalent and monovalent panel of anti-PD-1 antibodies with a range of affinities, against cell lines with a range of target densities. In calibrating the model to the in vitro binding data, we observed an affinity-dependent discrepancy between experimentally observed and model-predicted cell binding that we hypothesize arises due to unavoidable assay limitations. The calibrated model was then reused to correct for the assay bias and to generate refined estimates for on-cell antibody binding. The predictions generated by this model for the influence of avidity on cell surface receptor engagement with therapeutic antibodies may guide strategies for their structural engineering and dosing.