My daughter was miserable at public school, so we moved her to a private school. In the short term, it was a big improvement. The have her a grade skip. However, they were really against add skipping and we quickly realized they planned to make her repeat the grade rather than stay ahead. They didn't make her repeat it once they saw her standardized test scores, but we were unsure for a while. We found the private school to be as inflexible as the public school. So there were positives and negatives.
What I have found is that they are most willing to negotiate if they realize you might switch schools. I don't think it is a good idea to suggest a switch without meaning it, but I have found that schools offer quite a bit when they realize a child is leaving. When I moved my daughter to private school, the public school offered quite a few things they had never suggested before.
Anyway, the main thing is just to make sure to keep your options open. Try to keep a positive relationship with all of the schools and be careful of private school contracts that may make it difficult to switch. At the same time, negotiate before sending your child because they will be more flexible (in many cases) than once you have made a commitment.
