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 Alfv´en speed, the toroidal rotation shear drives a Kelvin-Helmholtzlike global plasma instability. Optimising the rotation profile to maximise the pressure before encountering external kink modes, but simultaneously avoiding flow-driven instabilities, can lead to a window of stability attractive for operating future high-performance fusion devices.