I just thought about an interesting situation :

The final horn sounds and team A won by 3 points. Team A then gets a technical foul. Since they cannot affect the result of the game, we don't administrate the 2 shots, right? But let's say team A gets another T... You see me coming. Both T's together would have given 4 free throws to team B, and therefore could have changed the result of the game! I know it will probably never happen, but just to know! I would say that we administrate the 4 FT. What do you think?

4 shots

That is one reason that I check the score quickly and get out.

Yep, shooting 4 throws. However, if the first two miss, no need to shot the other 2.

Thanks for your answers. We never know when something like that can happen!