A major goal of cancer research is to understand how mutations distributed across diverse genes affect common cellular systems, including multiprotein complexes and assemblies. Two challenges—how to comprehensively map such systems and how to identify which are under mutational selection—have hindered this understanding. Accordingly, we created a comprehensive map of cancer protein systems integrating both new and published multi-omic interaction data at multiple scales of analysis. We then developed a unified statistical model that pinpoints 395 specific systems under mutational selection across 13 cancer types. This map, called NeST (Nested Systems in Tumors), incorporates canonical processes and notable discoveries, including a PIK3CA-actomyosin complex that inhibits phosphatidylinositol 3-kinase signaling and recurrent mutations in collagen complexes that promote tumor proliferation. These systems can be used as clinical biomarkers and implicate a total of 548 genes in cancer evolution and progression. This work shows how disparate tumor mutations converge on protein assemblies at different scales.