Quite a few variables thrown around here. There is also MCL-max climb vs MCT max continuous.
Thrust rating is based on EGT for 5 mins at sea level and ambient temp of 35 degrees C for hot weather ops with no penalty. The cycles and conditions on the engine will decrease the EGT margins, thus decreasing time limits.
Specific procedures are designed, with different thrust time limits, for high-altitude airports or cold weather ops.
I seem to remember a few tricks, with AT on/off when sel TOGA, especially when OEI (and the double press).