Abstract Background Cells constantly sense many internal and environmental signals and respond through their complex signaling network, leading to particular biological outcomes. However, a systematic characterization and optimization of multi-signal responses remains a pressing challenge to traditional experimental approaches due to the arising complexity associated with the increasing number of signals and their intensities. Results We established and validated a data-driven mathematical approach to systematically characterize signal-response relationships. Our results demonstrate how mathematical learning algorithms can enable systematic characterization of multi-signal induced biological activities. The proposed approach enables identification of input combinations that can result in desired biological responses. In retrospect, the results show that, unlike a single drug, a properly chosen combination of drugs can lead to a significant difference in the responses of different cell types, increasing the differential targeting of certain combinations. The successful validation of identified combinations demonstrates the power of this approach. Moreover, the approach enables examining the efficacy of all lower order mixtures of the tested signals. The approach also enables identification of system-level signaling interactions between the applied signals. Many of the signaling interactions identified were consistent with the literature, and other unknown interactions emerged. Conclusions This approach can facilitate development of systems biology and optimal drug combination therapies for cancer and other diseases and for understanding key interactions within the cellular network upon treatment with multiple signals.