For NPC Sororities this is definitely possible since if you depledge, you were never initiated. The girl would have to wait one calendar year before getting another shot. She then could join any of the NPCs, even re-pledge the one she quit. Re-pledging the same house is rare and usually only happens if the reasons for depledging were out of her control. Ex. Parents force it on her.
For the IFC Fraternities, I believe it's possible for MOST of them. There's 63 of them, so it's hard to have a blanket answer. Ex. Kappa Alpha Psi and Iota Phi Theta are part IFC as well as NPHC. They probably go with the NPHC policy more often. (I'd guess.)
Depledging and re-rushing doesn't happen an awful lot, but it's not so rare that it would cause a huge concern.
Basically, it would depend on the campus and the number of chapters represented. A girl could be considered "tainted" (there's probably a more appropriate word, but...) if there's only, say four chapters. But if there's more like 16, then a chapter might easily ignore it. But as always, there could be situations that are exactly opposite.
De-pledging and Pledging Again
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