Systematically investigating the scores of genes mutated in cancer and discerning real drivers from inconsequential bystanders is a prerequisite for Precision Medicine, but remains challenging. Here, we developed a somatic CRISPR/Cas9 mutagenesis screen to study 215 recurrent long-tail breast cancer genes, which revealed epigenetic regulation as major tumor suppressive mechanism. We report that core or accessory components of the COMPASS histone methylase complex including KMT2C, KDM6A, BAP1 and ASXL2 (EpiDrivers) cooperate with PIK3CAH1047R to transform mouse and human breast epithelial cells. Mechanistically, we find that Cre-mediated activation of PIK3CAH1047R elicited an aberrant alveolar lactation program in luminal cells, which was exacerbated upon loss of EpiDrivers. Remarkably, EpiDriver loss in basal cells also triggered an alveolar-like lineage conversion and accelerated formation of luminal-like tumors, suggesting a basal origin for luminal tumors. As EpiDrivers are mutated in 39% of human breast cancers, lineage infidelity and lactation mimicry may significantly contribute to early steps of breast cancer progression.