You can't go any higher than TOGA on a 747-400.
A one-push GA only gives a 2000fpm climb at the required speed. A two push GA gives you full THR REF.
If you have Rolls Royce engines, selecting ALTernate EEC's could give you a lot more than you bargained for (That's why there are warnings in the manuals about selected ALTernate EEC's at full thrust). Definitely more than TOGA.
Rgds.
NSEU.