I fly the 747-400 and during a max derate and a high assumed temp scenario (D-TO2 58 degrees) with an engine out, it climbs like a dog even when light. My company allows discretion in increasing thrust on the remaining three. You will make the climb requirements, at a much slower rate, with the remaining 3 at the original thrust settings. On PCs I leave the original thrust setting because by the time I am airborne I should have already sorted out the amount of rudder required to keep her straight and more thrust would obviously change that.
I flew the EMB 145 series and if I remember correctly, the reason that the FADEC added power after sensing a engine failure was due to the fact that when reduced it was possible to still meet the 2 engine climb performance but needed the "reserve" thrust to make the SE requirements. It is certified that way....when the reserve power function was MEL'd, there was a weight penalty (may be confusing with the CRJ).
FO