That would depend on the private school. In my experience most of private schools mix lower functioning ASD kids with emotionally disturbed. Or on the other hand other literally want only Aspergers kids preferably with some extraordinary talent to make them look good. I have visited close to 15 private schools in NJ and those I knew were most appropriate my daughter ( she's 12 years old) turned us away because she got nervous at Intake and started stimming and couldn't concentrate on questions. Yet at home she'll ask about politics and can have nice conversation albeit short as she hates to talk. All her teachers love her as she learns and retains everything fast. Unfortunately you'll have to visit each school private or public and see for yourself. I was so excited a few times about some schools from what they had on their websites but when I visited I was horrified by the situation in school. I always ask to visit classes and try to interact with students. And if you can talk to parents of children in those programs. That usually gives you more information than what the administration claims. Good luck with your search!