That is exactly like BOAC and Mutt said on some types and companies. Some will set the reduced on FFRATS ( A "fancy 747" classic system). Should you need the full thrust available, FE would select GA and advance the Thrustlevers accordingly.
Again on some types the pilot will set FLEX or reduced thrust by selecting temperature and then selecting a detent on thrustlevers say Airbus and FLEX/MCT detent. Again TOGA thrust is available by just pushing thrustlevers forward.
The whole idea of reduced thrust or FLEX temperature or a fixed reduction in % of N1 or EPR like some manufacturers call it, is to save the engines. However full rated thrust is available and can be selected and any time.