I’ve been wondering the same thing. I know that the title “Monsignor” is just an honor given to a priest, and doesn’t mean a higher position. In fact many want to do away with it altogether.
According to Wikipedia the following persons use “The Very Reverend” in writing their name among Catholics:
Priests with various grades of jurisdiction above pastor (vicars general, judicial vicars, ecclesiastical judges, episcopal vicars, provincials of religious orders of priests, priors of monasteries, deans, vicars forance, archpriests, for instance)
Keep in mind this is a non-catholic source, so dont know how accurate it is.