...if the sums are done correctly, the derated/flex takeoff should be fine without increasing thrust.
At one airline, I had a really hard time trying to get this point across, as these folks were trying to 'use' techniques from a much older type in their present aircraft.
Specifically, they would cobb the remaining throttles toward max thrust in the event of an engine failure, and this would provide no end of problems with their new First Officers in training....and besides, I received the perverbial deer in the headlights look when I pointed out the specific reference in the aircraft AFM.
Well, at least they listened to reason, and modified the procedure.....finally.