The Drosophila melanogaster ovarian follicle cell lineage provides a powerful system for investigating how epigenetic changes contribute to differentiation. Downstream from an epithelial stem cell, follicle progenitors undergo nine mitotic cell cycles before transitioning to the endocycle and initiating differentiation. During their proliferative phase, follicle progenitors experience Lsd1-dependent changes in epigenetic stability that can be monitored using GAL4::UAS variegation. Eventually, follicle progenitors acquire competence to respond to Delta, a Notch ligand present in the environment, which signals them to cease division and initiate differentiation. The time required to acquire competence determines the duration of mitotic cycling and hence the final number of follicle cells. We carried out a screen for dominant modifiers of variegation spanning nearly 70% of Drosophila euchromatin to identify new genes influencing follicle progenitor epigenetic maturation. The eight genes found include chromatin modifiers, but also cell cycle regulators and transcription factors. Five of the modifier genes accelerate the acquisition of progenitor competence and reduce follicle cell number, however, the other three genes affect follicle cell number in an unexpected manner.