Some mutations in cancer cells can be exploited for therapeutic intervention. However, for many cancer subtypes, including triple-negative breast cancer (TNBC), no frequently recurring aberrations could be identified to make such an approach clinically feasible. Characterized by a highly heterogeneous mutational landscape with few common features, many TNBCs cluster together based on their ‘basal-like’ transcriptional profiles. We therefore hypothesized that targeting TNBC cells on a systems level by exploiting the transcriptional cell state might be a viable strategy to find novel therapies for this highly aggressive disease. We performed a large-scale chemical genetic screen and identified a group of compounds related to the drug PKC412 (midostaurin). PKC412 induced apoptosis in a subset of TNBC cells enriched for the basal-like subtype and inhibited tumor growth in vivo. We employed a multi-omics approach and computational modeling to address the mechanism of action and identified spleen tyrosine kinase (SYK) as a novel and unexpected target in TNBC. Quantitative phosphoproteomics revealed that SYK inhibition abrogates signaling to STAT3, explaining the selectivity for basal-like breast cancer cells. This non-oncogene addiction suggests that chemical SYK inhibition may be beneficial for a specific subset of TNBC patients and demonstrates that targeting cell states could be a viable strategy to discover novel treatment strategies.