Nobody here can or should stop you from applying a third time. But the schools will know it is your third try. Up to you if you want to spend the time and effort on this again. If you truly want the boarding school experience, I would expand your application list.
It is up to you if you even want to uproot what sounds like a good current situation. If you are happy, involved, and doing well where you are, maybe just embrace and make the most of that experience. College will be coming soon enough at this point.