It is specifically banned in Leviticus 18:18. "And you shall not take a woman as a rival wife to another (usually translated "to her sister"], uncovering her nakedness while the other is still alive."
Also, 1st and 2nd Samuel have a major theme of the danger of polygamy (although this theme spans the whole of the Old Testament. Although the patriarch and kings had multiple wives, this caused great suffering, including the fall of Israel.
However, a polygamous marriage is a true marriage, unlike a homosexual union - you are bound to the second wife as much as of the first, but the second marriage was a grave sin. It's like cutting off your hand, it's a sin but once it's done you simply no longer have a hand and that's the natural consequence.
I used to live in a country where it was legal... and the social consequences are very bad for the women and children. The metaphysical effect (which is reflected socially on the first wife) is that she, her husband, and her relationship is diminished... something is permanently altered... The essence of marriage is dissolved... and becomes twisted.
And it is adultery against her. She has the right to divorce.