My school hasn't really been "overcrowded", but they always accept more freshmen than they really have space for.
When I was in school, anyone who joined a fraternity was required to live in the house. The school depended on the fraternity system to take a certain percentage of the freshman class out of the dorm system. (Sororities were different - only a couple had houses, and only upperclasswomen could live in them.) The school also guaranteed housing for 4 years. So freshmen typically lived in crowded rooms (3 people in a double, etc), and one dorm had "lounge doubles" - they installed doors with locks on a few entry lounges, and made them into doubles.
As of next fall, all freshmen are being required to live on campus - they cannot live in fraternity houses. The school is building a new dorm to accommodate the increase in dorm population. This past fall, for the first time, a few fraternities extended non-residential bids, so they can keep their houses closer to full next year. Which should mean that since fraternity houses will only have to accommodate 3 years' worth of brothers instead of 4, the Greek system should grow. I guess we'll see
