The one that doesn't is Islamic polygamy, in which wives are chattel and a husband can acquire a new wife in about the same way that my neighbor adds a new cow to his dairy herd.
Your nightmare scenario assumes my daughter is powerless and a helpless and subservient pawn of her husband. Luckily, I did not raise my daughters to be those things.
Requiring consent would limit the lifestyle choices of the husband and his new bride--the old one would have no power to stop him, and would find taking it to court rather difficult since the definitions are always free (unstable). And, how dare you try to exclude a needy new wife (and baby!) from health benefits and housing!
Given the way polygamy has worked in the past, I'd say many first wives would find themselves hard-pressed by circumstances not only to accept the new defintions of marriage, but to put a good face on it--
The only way I see a woman maintaining a strong hand would be to insist that all property be in her name, and also insisting on a prenup that, on the event of a new wife, her "dowry" remains hers. These are typical marital contracts in a few Muslim countries.