Once I had an opera singer so loud that my Rode NT2 could not handle
it. Backing up was the solution back then. My guess is the lack of
definition by backing her from the mic is partially caused by
reflections of the room, see if it helps to hang a few blankets around
as padding to reduce room reflections:

-----------------------------------------------------blanket
*LOUD* girl --- plenty of distance --- mic
-----------------------------------------------------blanket

So much for a possible technical solution. I did however like the
headphone tip given earlier because it solves the problem at the source


Cheers,
Marc