Might be that our manual is misleading there, however we are encouraged not to advance the thrust lever if we use derate and encounter an engine failure, especially if mixing derate and assumed temperature. The performance is allways conservatively calculated for the one engine case anyway so there is no need to do that. Below the relevant excerpt from the FCOM.
Combination Fixed Derate and ATM
This method uses a takeoff thrust less than the fixed derate takeoff thrust by first selecting a fixed takeoff derate from the FMC. This derate takeoff thrust is then further reduced by assuming a temperature that is higher than the actual temperature. In this case, the thrust reduction authorized by most regulatory agencies is limited to 25% below any certified takeoff thrust rating.
While the ATM portion of the thrust reduction is not considered a limitation for takeoff, the fixed derate portion is. 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, thrust levers should not be advanced unless conditions are encountered during the takeoff where additional thrust is needed on both engines, such as windshear. A thrust increase beyond the fixed derate limit following an engine failure could result in loss of directional control.
To be honest the Vmcg case is normally academic as our V1s are way above Vmcg in all cases but reduced braking action or contaminated runway in which cases we are encouraged to use full rated thrust (derate is allowed, ATM not). And for some reason we do not use derate on the classic, only on the NG, never got an explanation why.