I hope I understand this correctly. Here's my idea based on the description.
Add two tables that both link to a student ID field on the student dimension table, not the fact table. One is whether the student ever had Title I status. The other is all the schools that a student ever attended.
Now when you choose your school and a Title I status of TRUE, you will see all students that ever had title I status that ever went to your school.
There are a couple modifications I can imagine depending on the specific question to be answered.