Yes, they will take more than one. In my private school graduating class of 311, we had:
-3 go to West Point
-1 go to USMAPS
-1 go to USCGA
-2 go to USNA from NAPS
-1 go to USNA foundation school
Also, one got an Appointment to USAFA but chose West Point instead.
Hope that sows how many...