Aviendha has a first-sister.

In all the conversations about Aviendha and Elayne I never hear anyone mention the fact that we know Aviendha has a first-sister, a sister born of the same mother as her. She's called Niella, she's got a husband of her own that at no point did Aviendha have to marry and when Niella puts off the white (she's gai'shain when the books start) she does not wed Rand. First-sisters within Aiel culture are a blood bond, they are women born of the same mother. To become first-sisters if you were near-sisters is to magically go through the process of being reborn as sisters of the same mother, re-creating the blood bond in a metaphysical way.

First-sisters are not the same as sister-wives. Sister-wives can obviously be first-sisters, but becoming a sister-wife in Aiel culture is at no point stated or indicated that it would also mean having to become first-sisters. Because again, first-sisters do not marry the same man unless they explicitly choose to. And we know this beyond the shadow of a doubt, because Aviendha has a first-sister.