I was also going to say, it definitely would not be illegal to finish out the school year at your current school where I am. I'd be really surprised if it was! I would ask your current school administration.
It does depend a lot on personality. But I would tend to want to leave my child in their current school unless they were extremely outgoing or very unhappy in their current school. Classes are so well established by that time of year, it would be hard to break into the friend groupings anyway. But if you have an opportunity for soccer, play groups, community ed type stuff local to you in the summer definitely pursue that.
My son was happiest in school that last month of school at that age. It was all outside stuff, field trips, creative & social stuff. It was literally the best month of school for him. And that was the year of school that led to homeschooling for him. Your little guy probably have fun no matter where he is at.