Highly recommend Manhattan Youth Ballet's August intensive. There's a choice between 1, 2 or 3 weeks in August. Best value is 3 weeks as they do have a performance at the end that you need to do all 3 weeks for. In addition to their usual faculty, they get many guest teachers from NYCB and ABT, most of whom are principal dancers. They also may get guests who teach Broadway jazz from various Broadway shows (the last time dd went, they had Robbie Fairchild teach something from American in Paris). It's usually pretty late in August so very easily stackable. The vast majority of the older kids are coming off other SIs.
The French Academie also has a choice of various weeks. Also an August program.
Danish Ballet Masters is 2 weeks for ages 15 and up
Fabrice Herrault does a short program every summer through Ailey Extension. It's also 2 weeks in August.
Irina and Maxim's SI is also short and can be stacked depending on when the first SI ends. It was 2 weeks when dd looked at it, but it conflicted with the last week of another SI. Never looked at it again.
BAE has 2 weeks in late August
Ellison's pas and his variations intensive are shorter and can be stacked with either his regular SI or other SIs.
Of course, there's also the Joffrey Ballet School if you need something earlier in the season. That was the first non-home school SI dd did. She did 2 weeks in June before their program gets very large (and before her home SI). The reputation is not fabulous in the ballet world, but she had very good instruction and plenty of attention. She actually gained a great deal in those 2 weeks.