N0m: In cultures where men have multiple wives (such as by Teimanim, Moroccan Jews and some other Sephardic and non-Ashkenazic communities), they don’t usually “date” American-style. They’re more old fashioned, closer to how Israeli Yidden and American Chasidim go about shidduchim (beshow types), than to the Western dating system.
Also, their wives are already aware that they could have sister-wives, and many already have a few. So it is hardly surprising to them.