Amazon Interview re-loop possible?

This question is for Bar raiser/ hiring manager.

I interviewed for L6, but was inclined for L5. It was a split loop. The recruiter said the HM’s feedback was good and pushed hard for L6, but the other feedback indicated L5. He wouldn’t share which interviewer dropped the ball. I could only guess it was the BR if it resulted in downleveling. Now I was told that the HM is open to re-loop (with another BR and rest of panel from his team), but need to check. Is this possible without cool off period? Has anyone done it?