Basal-like and luminal breast tumors have distinct clinical behavior and molecular profiles, yet the underlying mechanisms are poorly defined. To interrogate processes that determine these distinct phenotypes and their inheritance pattern, we generated somatic cell fusions and performed integrated genetic and epigenetic (DNA methylation and chromatin) profiling. We found that the basal-like trait is generally dominant and is largely defined by epigenetic repression of luminal transcription factors. Definition of super-enhancers highlighted a core program common in luminal cells but a high degree of heterogeneity in basal-like breast cancers that correlates with clinical outcome. We also found that protein extracts of basal-like cells are sufficient to induce a luminal-to-basal phenotypic switch, implying a trigger of basal-like autoregulatory circuits. We determined that KDM6A might be required for luminal-basal fusions, and we identified EN1, TBX18, and TCF4 as candidate transcriptional regulators of the luminal-to-basal switch. Our findings highlight the remarkable epigenetic plasticity of breast cancer cells.