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Cancer evolution poses a central obstacle to cure, as resistant clones expand under therapeutic selection pressures. Genome sequencing of relapsed disease can nominate genomic alterations conferring resistance but sample collection lags behind, limiting therapeutic innovation. Genome-wide screens offer a complementary approach to chart the compendium of escape genotypes, anticipating clinical resistance. We report genome-wide open reading frame (ORF) resistance screens for first- and third-generation epidermal growth factor receptor (EGFR) inhibitors and a MEK inhibitor. Using serial sampling, dose gradients, and mathematical modeling, we generate genotype-fitness maps across therapeutic contexts and identify alterations that escape therapy. Our data expose varying dose-fitness relationship across genotypes, ranging from complete dose invariance to paradoxical dose dependency where fitness increases in higher doses. We predict fitness with combination therapy and compare these estimates to genome-wide fitness maps of drug combinations, identifying genotypes where combination therapy results in unexpected inferior effectiveness. These data are applied to nominate combination optimization strategies to forestall resistant disease.