A method is described for applying the linear-stability-based amplification factor transport (AFT) transition model to the popular, two-equation shear stress transport (SST) eddy-viscosity model, yielding the SST-AFT framework. The turbulent kinetic-energy-equation is modified by introducing a new source term that improves its ability to maintain laminar flow without affecting its near-wall behavior in fully turbulent regions. This source term includes a turbulence suppression function that maintains laminar flow until the critical amplification factor is reached. Test cases using the SST-AFT model are presented for a zero-pressure-gradient flat plate and several airfoils, including a multi-element one. Predictions with SST-AFT compare favorably with experiment, confirming the potential capabilities of the new transition/turbulence framework.