If you look at the history of "similar" storms that is what has happened.
It's looking like Donna back in the '60's. She went through the Antilles, made landfall in Marathon (Keys) Fl with sustained winds of 145 mph; a strong Cat 4 went out in Gulf and came back and made another landfall at the same intensity in Naples/Ft. Myers Beach/Ft. Myers, went out in Gulf and re-emerged in the Carolina's as a Cat. 2.
I've heard more stories about Donna for those that have been in the area than Charley; it battered FL twice with the same intensity and the storm surge was much worse.