this ALMOST happened...

[APG]

Under all major codes in the USA, you would issue a double technical foul. You would NOT shoot free throw for the technical fouls. Double fouls go to the point of interruption, which in this cause would the free throws on the shooting foul.

I think this is the pertinent rules for FIBA

Art. 42 Special situations

42.1 Definition
In the same stopped-clock period which follows an infraction, special situations may arise when additional foul(s) are committed.

42.2 Procedure

42.2.1 All fouls shall be charged and all penalties identified.
42.2.2 The order in which all fouls occurred shall be determined.
42.2.3 All equal penalties against the teams and all double foul penalties shall be cancelled in the order in which they were called. Once the penalties have been cancelled they are considered as never having occurred.
42.2.4 The right to possession of the ball as part of the last penalty still to be administered shall cancel any prior rights to possession of the ball.