Well, as long as you involved her family why not go all in? Meet the guy and tell him to move on, that you won’t allow it. Find out who his family is and tell THEM. She wants to pretend she’s a male king in an ancient world with concubines? Hello, she is a woman living in modern society. There will be fall out. She’ll be upset? “Hello, Sweetheart,” you tell her, “you want a poly relationship, you have to earn it.” Everyone knows. And everyone doesn’t approve. Tell her you will stay married to her until the kids leave for college. That if she ever wants a divorce in that time, she has to earn that too. “But, Honey, given your lifestyle, the judge would grant me custody. Think hard. Think very hard.”