Hi Chris,
This is a tricky scenario. You are describing some of the features of "multitenancy." You can create cohorts to hold the students for each organization, and you can create one custom role for each organization that will be granted access to Configrable Reports. Then you create one Configurable Report for each organization, restricted to display only students who are members of that cohort. You will need to manually administer this role. For a relatively small number of organizations, this method works fairly well.
I hope this helps,
Elizabeth