My daughter was only able to accelerate a grade thanks to a Catholic school. She was very unhappy in kindergarten and the Catholic school agreed to allow her to transfer there mid year and to place her in first grade. Once she was there, it became clear that they intended to have her repeat first grade. However, they let her move up once they saw her standardized test scores. They didn't provide any differentiation while we was there (they told me that the next year's work would be harder, that Common Core was harder, etc,) and we moved her to a different public school later. However, she was happy there and I am grateful they gave her the opportunity to skip a grade that she wouldn't have had anywhere else. I think individual schools differ and some might have been more willi to provide differentiation. Part of the problem was that it was a very small school and there were limited options. I don't think anywhere else in our region would have allowed the grade skip; other schools even tried to convince us to have her repeat a grade to get back with her age cohort. So I'm very grateful to the Catholic school because the grade skip has worked out very well.