Epithelial-mesenchymal transition (EMT) and cancer stem cell (CSCs) formation are two fundamental and well-studied processes contributing to cancer metastasis and tumor relapse. Cells can undergo a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype or a complete EMT to attain a mesenchymal one. Similarly, cells can reversibly gain or lose 'stemness'. This plasticity in cell states is modulated by signaling pathways such as Notch. However, the interconnections among the cell states enabled by EMT, CSCs and Notch signaling remain elusive. Here, we devise a computational model to investigate the coupling among the core decision-making circuits for EMT, CSCs and Notch. Our model predicts that hybrid E/M cells are most likely to associate with stem-like traits and enhanced Notch-Jagged signaling – a pathway implicated in therapeutic resistance. Further, we show that the position of the 'stemness window' on the 'EMT axis' is varied by altering the coupling strength between EMT and CSC circuits, and/or modulating Notch signaling. Finally, we analyze the gene expression profile of CSCs from several cancer types and observe a heterogeneous distribution along the 'EMT axis', suggesting that different subsets of CSCs may exist with varying phenotypes along the epithelial-mesenchymal axis. We further investigate therapeutic perturbations such as treatment with metformin, a drug associated with decreased cancer incidence and increased lifespan of patients. Our mechanism-based model explains how metformin can both inhibit EMT and blunt the aggressive potential of CSCs simultaneously, by driving the cells out of a hybrid E/M stem-like state with enhanced Notch-Jagged signaling.