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Durable control of invasive solid tumors necessitates identifying therapeutic resistance mechanisms and effective drug combinations. In this work, we used a network-based mathematical model to identify sensitivity regulators and drug combinations for the PI3Kα inhibitor alpelisib in ER+ PIK3CA mutant breast cancer. The model-predicted efficacious combination of alpelisib and BH3 mimetics, e.g., MCL1 inhibitors, was experimentally validated in ER+ breast cancer cell lines. Consistent with the model, FOXO3 downregulation reduced sensitivity to alpelisib, revealing a novel potential resistance mechanism. Cell line-specific sensitivity to combinations of alpelisib and BH3 mimetics depended on which BCL-2 family members were highly expressed. Based on these results, newly developed cell line-specific network models were able to recapitulate the observed differential response to alpelisib and BH3 mimetics. This approach illustrates how network-based mathematical models can contribute to overcoming the challenge of cancer drug resistance.