Personalized therapy is a major goal of modern oncology, as patient responses vary greatly even within a histologically defined cancer subtype. This is especially true in acute myeloid leukemia (AML), which exhibits striking heterogeneity in molecular segmentation. When calibrated to cell-specific data, executable network models can reveal subtle differences in signaling that help explain differences in drug response. Furthermore, they can suggest drug combinations to increase efficacy and combat acquired resistance. Here, we experimentally tested dynamic proteomic changes and phenotypic responses in diverse AML cell lines treated with pan-PIM kinase inhibitor and fms-related tyrosine kinase 3 ($FLT3$) inhibitor as single agents and in combination. We constructed cell-specific executable models of the signaling axis, connecting genetic aberrations in $FLT3$, tyrosine kinase 2 ($TYK2$), platelet-derived growth factor receptor alpha ($PDGFRA$), and fibroblast growth factor receptor 1 ($FGFR1$) to cell proliferation and apoptosis via the PIM and PI3K kinases. The models capture key differences in signaling that later enabled them to accurately predict the unique proteomic changes and phenotypic responses of each cell line. Furthermore, using cell-specific models, we tailored combination therapies to individual cell lines and successfully validated their efficacy experimentally. Specifically, we showed that cells mildly responsive to PIM inhibition exhibited increased sensitivity in combination with PIK3CA inhibition. We also used the model to infer the origin of PIM resistance engineered through prolonged drug treatment of MOLM16 cell lines and successfully validated experimentally our prediction that this resistance can be overcome with AKT1/2 inhibition. Cancer Res; 77(4); 827–38.