As a Christian and teacher of the Word, I find myself at odds with polygamy and polyamory. Biblically speaking, there is precedent of multiple wives. Understanding the reason why is important. As a previous commenter stated, there is a tradition of patriarchy, and we need to remember that the patriarchy of Israel allowed multiple wives.
One of the "in-between-the-lines" laws of the levirate marriage implies that multiple wives is accepted and allowed. Here, this law states that if a woman's husband dies, she is to remarry his brother so that she will be protected and cared for, and also provide an heir to her dead husband.
As seemingly archaic as this is, today, in actuality, the brother could very well have been already married. This means that the brother would have been in a polygamous relationship as a result of the law.
David was given the wives of Saul. Why? Again, to protect and care for them. While the practice wasn't commonplace, as it would take wealth to marry multiple wives and care for the children, it was a practice.
Even in Jesus' time, the Sadducees came to Jesus to trap him in an argument, but used the levirate marriage as their source of entrapment. Jesus did not, as he should have if the law was wrong, refute the law itself, but the understanding of marriage in the post-resurrection world.
Here, I am making an argument about the ability of a man to have multiple wives, and yet I do not have more than one. I truly believe that the Bible does NOT forbid this practice. And several pastors skirt the issue, or argue the Pauline argument of a leader of the church being married to one wife. However, even then, the argument in the Greek would be the man of his first wife. In other words, a man married to his first wife (not divorced) could also be married to a second wife, and this would allow the leader to serve as a leader.
But now it gets sticky. People use the argument of Adam and Eve-- one plus one, not one plus two. Here, again, we find that Adam married again, and had more sons with the second wife.
Patriarchal or not, the idea is the same-- the care and treatment of the second wife as equal in value and rights as the first. Just because she was the second wife does not mean that she should be given second-class status.
And here is my belief, although I do not currently practice it because of the law-- a man may have multiple wives and it is not a sin. The legality of it in our current system is that it is not allowed and is punishable by fines and prison terms. So, we take one step backward into a polyamorous relationship. Those who value a poly relationship and are Christians should consider the equal love and care of the second "wife" as no better or worse than the first.
Here, the Bible does NOT contradict this relationship, except that in the eyes of God, the man is married to both women. Human laws can consider the rights and loss of rights based on registered domestic partnerships, marriages, etc., but even if the relationship were held among the three, or the blended family (kids) of the three, the fact that the man treats his wives well, with equal loving and care is the purpose of the relationship, modeling Christ's love for the church. Because the legal system in many countries sees this as a bad practice, and most of those also have laws against polygamy, the response really is that the church should step up and, if they accept the poly relationship, the church should not only encourage that the proper care and love and protections of the second "wife" are foremost in the poly relationship, they should also work diligently in the case of difficulty in the relationship.
So, from a Christian perspective, as poly is termed and how we understand polyamorous relationships, religious legality isn't in the eyes of man, but God, and God does not forbid such a relationship. The church should not ignore or turn their heads against the practice, but should do everything in their power to protect such fragile relationships and offer counseling to assist.
You've made mistakes, but you're doing your best.