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I'm not sure how it works as a general rule, but I do know the history of one chapter at the college I used to be at. Kappa Sigma Kappa was a local fraternity on campus. Theta Xi came and colonized. Don't remember the reasons, but they decided to merge. It ended up being Theta Xi so it could be national, but the chapter was Kappa Kappa so they could keep part of the "Kappa Sigma Kappa" alive. Worked out well.
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