Holding my child back in 9th grade

Are you sure private schools will do this? I work at a private school and we generally will not do this if kids have passed their grade at their previous school. Also, if he already did 9th and then does 9th again, you’ll have to report both 9th grades on college apps which is going to be strange. He also may not be allowed to retake HS level courses, whereas retaking MS level courses is fine.