Resistance to targeted cancer therapies is an important clinical problem. The discovery of anti-resistance drug combinations is challenging as resistance can arise by diverse escape mechanisms. To address this challenge, we improved and applied the experimental-computational perturbation biology method. Using statistical inference, we build network models from high-throughput measurements of molecular and phenotypic responses to combinatorial targeted perturbations. The models are computationally executed to predict the effects of thousands of untested perturbations. In RAF-inhibitor resistant melanoma cells, we measured 143 proteomic/phenotypic entities under 89 perturbation conditions and predicted c-Myc as an effective therapeutic co-target with BRAF or MEK. Experiments using the BET bromodomain inhibitor JQ1 affecting the level of c-Myc protein and protein kinase inhibitors targeting the ERK pathway confirmed the prediction. In conclusion, we propose an anti-cancer strategy of co-targeting a specific upstream alteration and a general downstream point of vulnerability to prevent or overcome resistance to targeted drugs.