@Mad, not for the big beast but for the small Boeing an interesting excerpt from our fcom:
Engine Failure during a Fixed Derate Takeoff (As Installed)
During a fixed derate takeoff, the takeoff speeds at low gross weights may not provide a safe operating margin to minimum control if the thrust levers are advanced beyond the fixed derate limit. A thrust increase beyond the fixed derate limit following an engine failure, could result in loss of directional control and should not be accomplished unless, in the opinion of the captain, terrain contact is imminent. This is because the takeoff speeds consider VMCG and VMCA at the fixed derate level of thrust.
Engine Failure during a Combined Takeoff (As Installed)
During a takeoff using both ATM and fixed derate methods of reduced thrust (Combined Takeoff), the takeoff speeds at low gross weights may not provide a safe operating margin to minimum control if the thrust levers are advanced beyond the fixed derate limit. This is because the takeoff speeds consider VMCG and VMCA only at the fixed derate level of thrust for the actual temperature. Since the crew has no indication where the fixed derate limit is, a thrust increase should not be accomplished unless in the opinion of the commander, terrain contact is imminent.
As derate is very common training therefore mandates not to touch the thrust setting and rather use the correct flying technique.