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Natural killer (NK) cells may be engineered with chimeric antigen receptors (CARs) to recognize tumor-associated antigens which bolsters their antitumor activity. More so than CAR-T cells, CAR-NK cell responses result from an integration of signals from a wider range of innate activating cytotoxic receptors, inhibitory receptors, and adhesion receptors in addition to the engineered CAR, making computational modeling of CAR-NK cell cytotoxicity more difficult than CAR-T cells. Uncovering mechanisms and predicting tumor cell responses to CAR-NK cytotoxicity is essential for improving therapeutic efficacy. The complexity of these effector-target interactions and the donor-to-donor variations in NK cell receptor (NKR) repertoire preclude the use of predictive models based on a single receptor, requiring function to be determined experimentally for each donor, CAR, and target combination. Computational modeling generates frameworks that allow the relationships of these factors to biologic outcomes to be explored without resource-consuming experiments. Here, we developed a computational mechanistic multiscale model which considers heterogenous expression of CARs, NKRs, adhesion receptors, and their cognate ligands, signal transduction, and NK cell-target cell population kinetics. The model is trained with quantitative flow cytometry and in-vitro cytotoxicity data and accurately predicts the short-term, long-term, and in-vivo cytotoxicity of CAR-NK cells. Furthermore, using Pareto optimization we explored the effect of CAR proportion and NK cell signaling on the differential cytotoxicity of CD33CAR-NK cells to cancer and healthy cells. This model can be extended to predict CAR-NK cytotoxicity across many antigens and tumor targets and serves as a tool to mechanistically explore CAR-NK signaling and biology.