Sheared toroidal rotation is found to increase the ideal external kink stability limit, thought to be the ultimate performance limit in fusion tokamaks. However, at rotation speeds approaching a significant fraction of the Alfvén speed, the toroidal rotation shear drives a Kelvin–Helmholtz-like global plasma instability. Optimizing the rotation profile to maximize the pressure before encountering external kink modes, but simultaneously avoiding flow-driven instabilities, can lead to a window of stability that might be attractive for operating future high-performance fusion devices such as a spherical tokamak component test facility.