Kelly Services was named in May by the School Reform Commission.
PA Cyber Charter had contracts with entities that were tied to the school's founder.
Like SLA, the new school will focus on project-based learning where students pose and solve their own problems.
The plaintiffs urged the justices to intervene, saying the current system has led to large inequities. Attorneys for the state contend that school funding is "political" and that the judiciary has no role.
A coalition of school districts, advocacy groups, and students is challenging the way the state pays for education.
Dozens of performers from across the state came together in music and song.
The justices will be asked to determine whether they should intervene. Gov. Wolf says no.