not enough rec letters?

You still have a few weeks before recruitment. Ask the people who wrote recs for you if they have friends who were in other sororities. I bet the do. Then CALL (not email, not text) those women and ask if you can drop off a resume so that they might write a rec for you, too. Also mention the name of the person who referred you. That's how I did it and within a week I had commitments for 7 more recs. They might not want to write one unless they meet you, which is why you drop off the resume if possible. And it's much easier to say no via text or email than if you are having a phone conversation with them.