Yes and no.
When I rushed, there were 4 national sororities and a local. The local did not participate in formal rush that year.
I had a definite favorite going into formal rush, and there was a second sorority that really impressed me during round 1. Both sororities invited me to round 2.
During round 2, I came to two conclusions. 1 - I really liked the idea of being part of a sisterhood; 2 - neither of these two sororities was the right choice for me. So I dropped out of rush.
The following week, the local held their rush, and I decided to drop by... and found my home