Clark School and The Phoenix School have rolling admission. I think both have slots for K now and in the fall. They have rolling admission. My son was 4.5 years old when we applied around Halloween. He's got a late birthday, but he was accepted to both schools immediately. Both schools allowed him to start as a pre-kindergarten student after Thanksgiving and be enrolled full-time as a kindergarten student next year.
Both the Clark School in Danvers and the Phoenix School in Salem are private gifted schools. I don't think they have cater specifically to the exceptional or profoundly gifted schools like the Sage School does.
Both the Clark School and the Phoenix School have some differences. The Phoenix School is a one-room schoolhouse situation that holds about 27 students from pre-kindergarten to 8th grade. The Clark School has about 100 students from pre-k/k to high school. They group kids in classrooms by age. My son is in Group A with the pre-k, kindergarten, and first graders.
The Clark School is aimed at kids with attentional issues (which my son has), executive functioning issues, and processing disorders, or mild learning disabilities; The Phoenix School is not. The Clark School has a structured, traditional curriculum. The Phoenix School has a more flexible curriculum.
I grew up near the Sage School. I looked at their website, but frankly didn't want to live near where I grew up again. The Sage School is also about double the cost of the Clark School, which was an factor for us. The Sage School doesn't address attentional issues either, which was probably the biggest consideration for us.