Technically if you go by the Bible... it is permissible for MEN to have more than one wife... and to have sex outside the marriage for procreation purposes... Women can not have more than one husband however. There is no where in the Bible that says marriage is between one man and one woman. And if you read the stories many of the most prominent figures in the bible had multiple wives and even slept with women they were not married to in order to have children if the wife/wives had not produced any.
The Ten Commandments, which are found in Ex. 20:1-17, never address the issue of polygamy and polygamy was part of life in the Old Testament. The New Testament teaches that Christians should honor God through monogamy (1 Cor 7:1-2, 1 Tim 3:2). There are scores of examples of monogamy being God?s preference for man:
Adam & Eve were designed monogamously (Gen. 2:24). No polygamy existed until 7 generations after Adam (Gen 4:19). Noah, the last righteous man of his day, had only one wife (Gen 7:13). Qualification for an elder (Tit 1:6) Qualification for a deacon (1 Tim 3:12) Qualification for a worthy widow (1 Tim 5:9) Every New Testament command for a husband or wife assumes monogamy in the commandments (Mk 10:12, 1 Cor 7:3, Eph 5:33, etc.). The comparison of Christ and the church to a husband and wife relies on a monogamous design for marriage (Eph 5:22-23).
1 Timothy 3; 2, 12 says: "The overseer should therefore be irreprehensible, a husband of one wife, moderate in habits, sound in mind, orderly, hospitable, qualified to teach. Let ministerial servants be husbands of one wife, presiding in fine manner over children and their own households". 1 Corinthians 7:2 says: "Yet, because of prevalence of fornication, let each man have his own wife and each woman have her own husband". Therefore, a man should only be married to one woman.
From the comments I read, it is well known that Solomon had many wives as well as concubines. But not everyone is aware that, in doing so, he was violating God's clearly stated commandment that the king "must not take many wives, or his heart will be led astray." (Deut. 17:17). It should also be noted that, because of the influence of his foreign wives, Solomon turned to the worship of false gods and " And The Lord was angry with Solomon, because his heart had turned away from the Lord, the God of Israel; who had appeared to him twice, and had commanded him concerning this thing, that he should not go after other gods; but he did not keep what The Lord commanded." ( 1 Kings 11:9-10) Revised Standard Version Solomon's sons suffered the consequences for his actions in later years, you can read further to answer what happened to Solomon's Kingdom. So, it was not permissible according to the Bible. The ones that did it were going against God, and did what they wanted. Just like today.