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While the effect of amplification-induced oncogene expression in cancer is known, the impact of copy-number gains on "bystander" genes is less understood. We create a comprehensive map of dosage compensation in cancer by integrating expression and copy number profiles from over 8000 tumors in The Cancer Genome Atlas and cell lines from the Cancer Cell Line Encyclopedia. Additionally, we analyze 17 cancer open reading frame screens to identify genes toxic to cancer cells when overexpressed. Combining these approaches, we propose a class of 'Amplification-Related Gain Of Sensitivity' (ARGOS) genes located in commonly amplified regions, yet expressed at lower levels than expected by their copy number, and toxic when overexpressed. We validate RBM14 as an ARGOS gene in lung and breast cancer cells, and suggest a toxicity mechanism involving altered DNA damage response and STING signaling. We additionally observe increased patient survival in a radiation-treated cancer cohort with RBM14 amplification.