The TO/GA switches are inhibited when on the ground and enabled again when in the air for a go–around or touch and go.
Interesting interpretations: Where do you set a bounced landing in reference of inhibiting TOGA? And is bouncing airborne again considered "in the air", or "touch and go"?
It is not crystal clear and i remember me pushing the switches multiple times and shoving up the levers in the sim with a similar scenario to finally get TOGA .....
(Ahhhh, wishing back the spring-loaded firewall switch of the MD11: Shove the levers through the spring resistance and the AP and AT go off, max available thrust kicks in, FD commands wings level and max nose up and no automatic reversal whatsoever happens until the pilot switches stuff back on to his liking.
That could save your day.)