interschool

As a noun school

is a group of fish or a group of marine mammals such as porpoises, dolphins, or whales or school can be (us|canada)  an institution dedicated to teaching and learning; an educational institution.

As a verb school

is (of fish) to form into, or travel in a school or school can be to educate, teach, or train (often, but not necessarily, in a school).

As an adjective interschool is

occurring or taking place between two or more schools.