The DNA damage response (DDR) ensures error-free DNA replication and transcription and is disrupted in numerous diseases. An ongoing challenge is to determine the proteins orchestrating DDR and their organization into complexes, including constitutive interactions and those induced by genomic insults. Here we use multi-conditional network analysis to systematically map DDR assemblies at multiple scales. Affinity purifications of 21 DDR proteins, with/without genotoxin exposure, are combined with multi-omics data to reveal a hierarchical organization of 605 proteins in 109 assemblies. Assemblies capture canonical repair mechanisms and propose new DDR-associated proteins extending to stress, transport, and chromatin functions. We find significant associations between protein assemblies and genetic dependencies in processing different genotoxic agents and that multiple-assembly proteins can act pleiotropically in multiple-agent responses. Protein assignments are further supported by specific DDR readouts, implicating twelve new proteins in double-strand-break repair. The DNA Damage Response Assemblies Map is available for interactive visualization and query (ccmi.org/DDRAM/).