In both vertebrates and insects, neurons typically arise from neural stem cells or terminally dividing intermediate progenitors. Here, we describe another mode of neurogenesis where neural stem cells generate secondary precursors that undergo multiple rounds of self-renewing transit-amplifying divisions. We identify the Posterior Asense-Negative (PAN) neuroblasts, which do not express the transcription factors Asense or Prospero. PAN neuroblasts rely on the segregating determinants Numb and Brat to generate smaller, secondary neuroblasts that in turn give rise to ganglion mother cells (GMCs) and neurons throughout larval development. In brat or numb mutants, misspecified secondary neuroblasts are unable to produce differentiated progeny and initiate tumor-like overgrowth. In prospero mutants, however, tumors arise from GMCs while secondary neuroblasts are correctly specified. Our data describe a transit-amplifying lineage in the Drosophila nervous system and suggest that different vulnerabilities in intermediate cell types can affect the outcome of tumor suppressor loss in stem cell lineages.