Notch pathway is an evolutionarily conserved cell–cell communication mechanism governing cell-fate during development and tumor progression. It is activated when Notch receptor of one cell binds to either of its ligand—Delta or Jagged—of another cell. Notch–Delta (ND) signaling forms a two-way switch, and two cells interacting via ND signaling adopt different fates—Sender (high ligand, low receptor) and Receiver (low ligand, high receptor). Notch–Delta–Jagged signaling (NDJ) behaves as a three-way switch and enables an additional fate—hybrid Sender/Receiver (S/R) (medium ligand, medium receptor). Here, by extending our framework of NDJ signaling for a two-cell system, we show that higher production rate of Jagged, but not that of Delta, expands the range of parameters for which both cells attain the hybrid S/R state. Conversely, glycosyltransferase Fringe and cis-inhibition reduces this range of conditions, and reduces the relative stability of the hybrid S/R state, thereby promoting cell-fate divergence and consequently lateral inhibition-based patterns. Lastly, soluble Jagged drives the cells to attain the hybrid S/R state, and soluble Delta drives them to be Receivers. We also discuss the critical role of hybrid S/R state in promoting cancer metastasis by enabling collective cell migration and expanding cancer stem cell (CSC) population.