Dedifferentiated liposarcoma (DDLS) is a rare but aggressive cancer with high recurrence and low response rates to targeted therapies. Increasing treatment efficacy may require combinations of targeted agents that counteract the effects of multiple abnormalities. To identify a possible multicomponent therapy, we performed a combinatorial drug screen in a DDLS-derived cell line and identified cyclin-dependent kinase 4 (CDK4) and insulin-like growth factor 1 receptor (IGF1R) as synergistic drug targets. We measured the phosphorylation of multiple proteins and cell viability in response to systematic drug combinations and derived computational models of the signaling network. These models predict that the observed synergy in reducing cell viability with CDK4 and IGF1R inhibitors depends on the activity of the AKT pathway. Experiments confirmed that combined inhibition of CDK4 and IGF1R cooperatively suppresses the activation of proteins within the AKT pathway. Consistent with these findings, synergistic reductions in cell viability were also found when combining CDK4 inhibition with inhibition of either AKT or epidermal growth factor receptor (EGFR), another receptor similar to IGF1R that activates AKT. Thus, network models derived from context-specific proteomic measurements of systematically perturbed cancer cells may reveal cancer-specific signaling mechanisms and aid in the design of effective combination therapies.