Epithelial to Mesenchymal Transition (EMT) has been associated with cancer cell heterogeneity, plasticity and metastasis. However, the extrinsic signals supervising these phenotypic transitions remain elusive. To identify microenvironmental signals controlling cancer-associated phenotypes amid the EMT continuum, we defined a logical model of the EMT cellular network that access the qualitative degrees of cell adhesions by adherent junctions and focal adhesions, two features affected during EMT. Model attractors could recover epithelial, mesenchymal and hybrid phenotypes. In silico simulations provided evidences that hybrid phenotypes may arise through independent molecular paths, involving stringent extrinsic signals. Of particular interest, model predictions and their experimental validations indicated that: 1) ECM stiffening is a prerequisite for cells overactivating FAK-SRC to upregulate SNAIL1 and acquire a mesenchymal phenotype, and 2) FAK-SRC inhibition of cell-cell contacts through the Receptor Protein Tyrosine Phosphates kappa leads to the acquisition of a full mesenchymal rather than a hybrid phenotype. Altogether, our computational and experimental approaches permitted to identify critical microenvironmental signals controlling hybrid EMT phenotypes, and indicated that EMT involves multiple molecular programs.