A major challenge in developing anticancer therapies is determining the efficacies of drugs and their combinations in physiologically relevant microenvironments. We describe here our application of “constrained fuzzy logic” (CFL) ensemble modeling of the intracellular signaling network for predicting inhibitor treatments that reduce the phospho-levels of key transcription factors downstream of growth factors and inflammatory cytokines representative of hepatocellular carcinoma (HCC) microenvironments. We observed that the CFL models successfully predicted the effects of several kinase inhibitor combinations. Furthermore, the ensemble predictions revealed ambiguous predictions that could be traced to a specific structural feature of these models, which we resolved with dedicated experiments, finding that IL-1α activates downstream signals through TAK1 and not MEKK1 in HepG2 cells. We conclude that CFL-Q2LM (Querying Quantitative Logic Models) is a promising approach for predicting effective anticancer drug combinations in cancer-relevant microenvironments.