Computational analysis of cancer pharmacogenomics data has resulted in biomarkers predictive of drug response, but the majority of response is not captured by current methods. Methods typically select single biomarkers or groups of related biomarkers but do not account for response that is strictly dependent on many simultaneous genetic alterations. This shortcoming reflects the combinatorics and multiple-testing problem associated with many-body biologic interactions. We developed a novel approach, Multivariate Organization of Combinatorial Alterations (MOCA), to partially address these challenges. Extending on previous work that accounts for pairwise interactions, the approach rapidly combines many genomic alterations into biomarkers of drug response, using Boolean set operations coupled with optimization; in this framework, the union, intersection, and difference Boolean set operations are proxies of molecular redundancy, synergy, and resistance, respectively. The algorithm is fast, broadly applicable to cancer genomics data, is of immediate use for prioritizing cancer pharmacogenomics experiments, and recovers known clinical findings without bias. Furthermore, the results presented here connect many important, previously isolated observations.