I would say that the man is married to all of his wives.
Not the ideal, as in one man, one woman, but at that time and place, polygamy was culturally acceptable, and multiple wives were viewed positively because of the numerous children.
However, the man is disqualified from being a Deacon, Elder, Pastor, Bishop because he is not the husband of one wife.
And, the Bible says to remain in whatever state one is when one becomes saved, and in verse 29 below, the plural "wives" in used.
17 But as God hath distributed to every man, as the Lord hath called every one, so let him walk. And so ordain I in all churches.
18 Is any man called being circumcised? let him not become uncircumcised. Is any called in uncircumcision? let him not be circumcised.
19 Circumcision is nothing, and uncircumcision is nothing, but the keeping of the commandments of God.
20Let every man abide in the same calling wherein he was called.
21 Art thou called being a servant? care not for it: but if thou mayest be made free, use it rather.
22 For he that is called in the Lord, being a servant, is the Lord's freeman: likewise also he that is called, being free, is Christ's servant.
23 Ye are bought with a price; be not ye the servants of men.
24 Brethren, let every man, wherein he is called, therein abide with God.
25 Now concerning virgins I have no commandment of the Lord: yet I give my judgment, as one that hath obtained mercy of the Lord to be faithful.
26 I suppose therefore that this is good for the present distress, I say, that it is good for a man so to be.
27 Art thou bound unto a wife? seek not to be loosed. Art thou loosed from a wife? seek not a wife.
28 But and if thou marry, thou hast not sinned; and if a virgin marry, she hath not sinned. Nevertheless such shall have trouble in the flesh: but I spare you.
29 But this I say, brethren, the time is short: it remaineth, that both they that have wives be as though they had none;
1 Corinthians 7:17-29, KJV
There are muslim men here, who have up to four wives (all that is permitted under modern muslim law). In all cases I'm aware of, all or all but one marriage occurred in another country.
Under State law, he is only married to the first wife, and only his first wife and the children from her, count for government benefits, etc. If he was already married when he got married here, the State treats the marriage here as bigamy because he wasn't legally able to marry under State law.
However, under State law, he must provide for all of his biological children financially.
Many muslim men in this position get four-plexes and each wife has her own place, and he decides where he will spend each night. In reality, there is usually a schedule unless there's sickness, a special occasion, pregnancy, or trying to get pregnant. Or favorite(s). Some polygamous families have family dinners, study time, etc. together, share chores, etc., and rotate which home. Or the Senior Wife (usually the first wife, but not always) decides who does what, where.