If you marry more than one man or one woman its committing adultery.
What verse says this?
To know what the Bible really says about this lets contrast the stories of David and Abigail, with David and Bathsheba. In both relationships David was already married, but God sent a prophet in only one of them. Why is that? The reason is that David took Bathsheba while her husband was still alive, thus committing adultery. With Abigail, God killed her husband and only after did David take her as a wife.
In both cases David was already married, so his status is not important. However the status of the woman is significant. Abigail was available, and Bathsheba was not. David was rebuked after Bathsheba, but not Abigail.
The Biblical meaning of the sin of adultery is relations with a woman that is someone else's wife.