>>543212159
It was a bunch of schools, at least six.
The tea party are the main three but there's also the sisterhood, knights hospittler, Johannes faction, and arius was supposed to join

Hyakki was also a bunch of smaller schools that joined together over time.

Kivotos literally has thousands of schools according to Rin. If you want any sort of power you need to make alliances and join together with other similar schools.

Reminder that there are thousands of academies in kivitos, sensei so far has only had time to visit the central schools.