There are several stories of polygamy in the Bible, and they almost all turn out badly.
In Genesis 29 (see this learning for the complete story), Jacob has fled Canaan from his murderous brother Esau after deceptively obtaining Esau's blessing from Isaac.
He makes his way to Haran, to his uncle Laban's house. There he ends up marrying Laban's two daughters, Leah and Rachel, as well as their two handmaidens, Bilhah and Zilpah. But he only married Leah because he was tricked into it, and as verse 29:31 records, Leah was hated.
Some translations offer the nicer "unloved" or "not loved," but the literal Hebrew is quite clearly hate.
Reading through this chapter, and the explanations that Leah gives to the names each of her children receives, it's heart-wrenching to see what it can be like for one wife when a different wife is clearly preferred by her husband.
And when they're sisters, of course, it's that much worse.
This dynamic doesn't end - the children of Rachel are preferred by Jacob to the children of Leah, leading to a lot of resentment and ultimately the brothers' selling Joseph (Rachel's son) down to Egypt.
Later on in the Bible, the reality that it's not such a good idea to marry two sisters is turned into a proper prohibition:
"You shall not take a woman as a wife after marrying her sister, as her rival, to uncover her nakedness beside the other during her lifetime." (Vayikra 18:18)