That’s actually what Greek chapters are right now. Chapter funding comes from members’ dues and fundraising, not from the university, and are considered to be private, as each chapter is regulated individually by their national headquarters. At most universities (the only exceptions I know of being very small schools…

That’s exactly what they are right now. Greek chapters are considered “private” as they are not supported by university funds, but instead by members’ annual dues and fundraising. Greek houses are usually located in a “Greek town” which is considered to be off-campus by the university (Example: every time it snowed…