Differentiation events contribute to phenotypic cellular heterogeneity within tumors and influence disease progression and response to therapy. Here, we dissect mechanisms controlling intratumoral heterogeneity within triple-negative basal-like breast cancers. Tumor cells expressing the cytokeratin K14 possess a differentiation state that is associated with that of normal luminal progenitors, and K14-negative cells are in a state closer to that of mature luminal cells. We show that cells can transition between these states through asymmetric divisions, which produce one K14+ and one K14− daughter cell, and that these asymmetric divisions contribute to the generation of cellular heterogeneity. We identified several regulators that control the proportion of K14+ cells in the population. EZH2 and Notch increase the numbers of K14+ cells and their rates of symmetric divisions, and FOXA1 has an opposing effect. Our findings demonstrate that asymmetric divisions generate differentiation transitions and heterogeneity, and identify pathways that control breast cancer cellular composition. Display omitted •Triple-negative breast cancers display phenotypic cellular heterogeneity•Asymmetric divisions that produce K14+ and K14− daughter cells generate heterogeneity•K14+ cancer cells display a progenitor-associated tumorigenic phenotype•EZH2, Notch, KLF5, and NFIB increase K14+ cell numbers and FOXA1 decreases them Granit et al. study the sources of phenotypic cellular heterogeneity in triple-negative breast cancers. They find that cancer cells can undergo asymmetric divisions that produce K14+ and K14− daughters and thereby generate heterogeneity. K14+ cells possess a progenitor-associated, tumorigenic phenotype, and the authors identify regulators that control their relative numbers.