I may have missed it, but I can find no passage of Scripture that prohibits a man from having more than one wife. It is true that Church leaders are to have only one (1 Tim. 3:2; Titus 1:5-6), but if Paul had his way, they wouldn't even have one (1 Cor. 7:1, 11, 20, 27-28, 32, etc.). There are several passages that speak against divorcing a wife to marry another woman, but I find none saying a man cannot marry additional wives.
In the Old Testament, God calls Israel His wife (Ezek. 16). Hosea's on-again, off-again marriage relationship to Gomer, an unfaithful wife, is a description of God's marriage relationship with Israel. He is even said to divorce Israel in Jeremiah 3:8-22, but in the end, He promises to bring her back to Himself (Rom. 9 - 11). In the New Testament, the Church is referred to as the bride of Christ; the relationship between Jesus, the Bridegroom, and the Church, the bride, which is to be our model for our own marriage (Eph. 5:22-32).
One might also look at the life of Jacob, to see, perhaps, a picture of the Triune God having two brides. If one sees Leah as a type of Israel, and Rachel as a type of the Church, one could easily come to the conclusion that the New Jerusalem, which descends from heaven adorned as a bride, is actually two brides: Israel is the twelve gates representing the twelve Tribes of Israel (Rev. 21:12), and the Church is twelve foundations representing the twelve Apostles (Rev. 21:14).
What I have written is not doctrine, but one simple mind trying to understand God' Word.