Mary, first, there are plenty of 5,000-student colleges - and those with fewer students - where Greek groups flourish. There are many where Greeks have NO housing, not even a chapter room, and they flourish. After all, it's all about the sisterhood?brotherhood, not a place to lay a rug.
That said, what happens is that somebody's apartment or personal rented house usually winds up being "the house," where the latest composite is hung and committee meetings are held, usually because a bunch of members live there.
Chapter meetings and recruitment events happen in clasrooms. So...it CAN work.
Frankly, I sincerely doubt that each Greek group has enough members to financially support a house. There are different kinds of housing, though, so you might want to check out lodges and similar arrangements.
Your first stop should be your fraternity housing officer. In the meantime, Greek alumnae need to be making the university administration aware of their support of Greek life. As they say, follow the money!

Much good luck to you!