For 737, you never get any sort of take-off thrust (either with or without derate) after pressing TOGA when airborne. It won't cancel anything out, it will completely change mode:
After airborne you get GO AROUND THRUST limit. Nothing more nothing less.
...and be very aware that if the throttles are still in hold (THR HLD, i.e. below 800 feet), you do NOT get any increase in thrust what so ever! Only the N1 limit bugs will move, but since the throttle is in hold, it will stay at the takeoff thrust selected (with derates/assumes etc.). Hence, you would then have to move the throttles yourself - either to the N1 limit bug, or firewall as needed - this is really something any 737 pilot must know.
Above 800 feet, the auto throttle changes to ARM. That mean the auto throttle is now able to move the thrust levers if so commanded. Pressing TOGA above 800 thereby changes thrust limit to GA (as indicated by the N1 limit bugs moving to that limit), and the thrust will automatically advance.
Here is what Boeing has to say about it:
Note: During a reduced thrust takeoff, a second press of the TO/GA switch below 800 feet above field elevation will change the thrust limit mode to GA and N1 reference bugs to increase to full GA thrust, thrust levers will not be in motion. A second press of the TO/GA switch above 800 feet above field elevation, thrust levers advance toward full GA thrust.
(With second press they are referring to the initiation of the takeoff roll as the FIRST press).
Above 2000 and flaps retracted (which ever is later), NOTHING will happen if you press the TOGA switch.