NCAA - Double T's

[Lotto]

The only thing I could find that speaks somewhat to this is:

A.R. 22. One or both foul(s) of either a multiple personal foul or a double personal foul is flagrant.
RULING: For a multiple personal foul, one free throw shall be awarded for each non-flagrant personal foul (women: non-flagrant foul) and two free throws shall be awarded for the flagrant personal foul (women: flagrant foul). For a double personal foul, no free throws shall be awarded. In either case, any player who commits a flagrant personal foul (women: flagrant foul) shall be ejected.

The implication seems to be that there are no free throws even if the nonflagrant foul would have carried a lesser penalty than the flagrant foul. It's a little bit of a stretch, but this leads me to think that you'd go POI.