Chemical perturbation screens offer the possibility to identify actionable sets of cancer-specific vulnerabilities. However, most inhibitors of kinases or other cancer targets result in polypharmacological effects, which complicate the identification of target dependencies directly from the drug-response phenotypes. In this study, we developed a chemical systems biology approach that integrates comprehensive drug sensitivity and selectivity profiling to provide functional insights into both single and multi-target oncogenic signal addictions. When applied to 21 breast cancer cell lines, perturbed with 40 kinase inhibitors, the subtype-specific addiction patterns clustered in agreement with patient-derived subtypes, while showing considerable variability between the heterogeneous breast cancers. Experimental validation of the top predictions revealed a number of co-dependencies between kinase targets that led to unexpected synergistic combinations between their inhibitors, such as dasatinib and axitinib in the triple-negative basal-like HCC1937 cell line.