Take the case of an engine rated at 26k, derated to 22k and reduced to 50C or any degree of derate/reduction in between.
Pressing the TOGA button for a second time will simply give you G/Around power for the selected derate/temperature combination selected in the FMC.
2XL, in answer to your specific question; To get 26k you will need to manually push the thrust levers forward to the N1 you noted earlier during your pre departure briefing. (you did make a note of the 26k N1, didn't you?)
The power will automatically and gradually revert to full rated power at FL 150 (watch it change from R/CLB to CLB as you pass 150 next time)
To regain full power earlier, as mentioned, delete the CLB 1 or CLB 2 reduction from the FMC when full CLB power will be restored.
I have to ask though, why would you want to restore full power any earlier than that in the event of a normal take off or even if you have an engine failure? In the first case all climb considerations are covered, in the second you are climbing to MSA and will, in all liklyhood, return to the field of departure.
Being given a direct routing over high terrain or to get over bad weather on departure would be two good reasons to delete the reduction but otherwise, I don't see the point.