Question
Would like to provide a service to schools where create extracurricular student groups in which the children would start a business and run it and revenue generated from the student business would help provide extra funding for the school.. Can schools own a business.
Answer
In theory they could own the business as long as the profit of that business were used to further the non-profit work of the school.
The bigger question would be whether the school actually owns the business or whether you as a separate non-profit were operating within the facilities of the school.