For high school, or already in HS and switching for 10th or 11th? My DD did this between 8th and 9th, at her instigation, from one top private to another, academically really no difference and the reasons were social and athletic, in these small schools, the atmosphere in a particular class can be a good fit or not. It was a very good move for her, and not difficult at all, and I know of other kids her year and other years that went in the same direction or in reverse, the schools seem completely open to it, and did not manufacturer any barriers. I know of kids that have done it between 9th and 10th as well, after that I think it is more difficult and probably not as good an idea, since will need ongoing relationships with teachers, college counselors to navigate the college process, and also leadership positions in extracurriculars, which will be perhaps more difficult to obtain if suddenly in a new school for 11th grade.
If your kid wants to do this, and can explain why in a coherent manner, and persists in the idea, then you should support it. 11th and 12th grade are stressful enough without adding social unhappiness to the mix. Can also explore this in the fall and won't need to make a decision until March or April, who knows, maybe all will be better and he won't want to leave in the end, but in the meantime, try to be supportive.