Epithelial-to-Mesenchymal Transition (EMT) and its reverse - Mesenchymal to Epithelial Transition (MET) - are hallmarks of cellular plasticity during embryonic development and cancer metastasis. During EMT, epithelial cells lose cell-cell adhesion and gain migratory and invasive traits either partially or completely, leading to a hybrid epithelial/mesenchymal (hybrid E/M) or a mesenchymal phenotype respectively. Mesenchymal cells move individually, but hybrid E/M cells migrate collectively as observed during gastrulation, wound healing, and the formation of tumor clusters detected as Circulating Tumor Cells (CTCs). Typically, the hybrid E/M phenotype has largely been tacitly assumed to be transient and 'metastable'. Here, we identify certain 'phenotypic stability factors' (PSFs) such as GRHL2 that couple to the core EMT decision-making circuit (miR-200/ZEB) and stabilize hybrid E/M phenotype. Further, we show that H1975 lung cancer cells can display a stable hybrid E/M phenotype and migrate collectively, a behavior that is impaired by knockdown of GRHL2 and another previously identified PSF - OVOL. In addition, our computational model predicts that GRHL2 can also associate hybrid E/M phenotype with high tumor-initiating potential, a prediction strengthened by the observation that the higher levels of these PSFs may be predictive of poor patient outcome. Finally, based on these specific examples, we deduce certain network motifs that can stabilize the hybrid E/M phenotype. Our results suggest that partial EMT, i.e. a hybrid E/M phenotype, need not be 'metastable', and strengthen the emerging notion that partial EMT, but not necessarily a complete EMT, is associated with aggressive tumor progression.