Mix progenitors are short-lived multipotential cells formed as intestinal epithelial stem cells initiate a differentiation program. Clone dynamics indicates that various epithelial cell lineages arise from Mix via a sequence of progressively restricted progenitor states. Lateral inhibitory Notch signaling between the daughters of Mix (DOM) is thought to break their initial symmetry, thereby determining whether a DOM invokes a columnar (absorptive) or granulocytic (secretory) cell lineage program. This is supported by the absence of granulocytes following enforced Notch signaling or Atoh1 deletion. Conversely, granulocytes increase in frequency following inhibition of Notch signaling or Hes1 deletion. Thus reciprocal repression between Hes1 and Atoh1 is thought to implement a Notch signaling-driven cell-fate-determining binary switch in DOM. The brush (tuft) cells, a poorly understood chemosensory cell type, are not incorporated into this model. We report that brush cell numbers increase dramatically following conditional Atoh1-deletion, demonstrating that brush cell production, determination, differentiation and survival are Atoh1-independent. We also report that brush cells are derived from Gfi1b-expressing progenitors. These and related results suggest a model in which initially equivalent DOM progenitors have three metastable states defined by the transcription factors Hes1, Atoh1, and Gfi1b. Lateral inhibitory Notch signaling normally ensures that Hes1 dominates in one of the two DOMs, invoking a columnar lineage program, while either Atoh1 or Gfi1b dominates in the other DOM, invoking a granulocytic or brush cell lineage program, respectively, and thus implementing a cell fate-determining ternary switch.