In some cultures, men can take wives and the other wives will not be able to say yea or nay on the matter. 
The man will go off, acquire a new bride, bring her home and everyone is expected to adjust accordingly. 
This seems, to me, to leaves wives in a position to where they have no say over who they will build a family with.
That type of polygyny makes me sad. We don’t have to be in any way alike, we don’t have to like any of the same things. We can be our own types of people. All I ask for is a team-player mentality, the WANT to build this empire for the betterment of all of us.
 

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There are women who are preaching that NO, the existing wives should have NO SAY. I SUSPECT it’s because they themselves are recently acquired wives and perhaps the existing wives were saying no to her being the one to join the family. And the husband invoked his “you have no say”-ness to it, and married her anyway. These women have no loyalty to the Universal Sisterhood of All Women, which dictates that you don’t allow these kinds of things to happen to your sister. You don’t allow her “choice” to be taken away.

What about existing wives in monogamy that DONT want a polygynous relationship?
YOU SHOULD NEVER EVER FORCE THEM. Even if you feel as if it’s your God-given right! YOU DONT DO IT. You’ve already got a wife. You should love her in the same way that you love yourself! You’d never FORCE yourself in such a situation. No — you value yourself TOO MUCH for that!
You can try convincing her, you can educate her on it, you can insist she read up on it and at least CONSIDER changing her view of it. But if she’s a decent wife, caring for house and home…and loving you…there’s no reason other than selfishness to steamroll past her dislike of polygyny. Don’t hurt that relationship with her for something that MAY NOT WORK OUT ANYWAY, thanks to the brokenness of people’s minds today.
You’ll be like that dog who had a small bone and when he looked in the water he saw a dog with a larger bone. He was unaware that this was his reflection and decided that he wanted THAT dogs bone. But in order to get THAT larger bone, he’d have to drop his own bone. So he let out a fierce bark and dropped his bone. He went after what he saw as the larger bone, and lost his small bone in the process. When he jumped in the water, the dog he saw, and it’s larger bone, disappeared.
…You don’t do that.

Please. Allow your wives to have a say. When they say it, dig into why they feel the way they feel and give it a consideration. You owe it to them, because you’d want people to do that for you in such a MAJOR situation (because taking on wives is NOT child’s play — wives are people with feelings, emotions, personalities, mindsets, etc and they deserve respect and consideration).