It is allowed for Muslim men that they can have more than 1 wives and they can marry upto four provided that they do justice with all of them.Allah swt says in Holy Quran:
Marry women of your choice, two or three, or four but if you fear that you shall not be able to deal justly (with them), then only one or (the captives and the slaves) that your right hands possess. That is nearer to prevent you from doing injustice. (An-Nisa 4:3)
Justice is an obligation on Muslim men and they will be accountable before Allah swt if they do injustice .But this has to be kept in mind that Quantitative justice is more important than qualitative justice which means a man must try to distribute his resources and time equally among his wives but if he has more love for one among them he will not be accountable for it.
Allah swt says in Holy Quran:
You will never be able to do perfect justice between wives even if it is your ardent desire, so do not incline too much to one of them (by giving her more of your time and provision) so as to leave the other hanging (i.e. neither divorced nor married). And if you do justice, and do all that is right and fear Allâh by keeping away from all that is wrong, then Allâh is Ever Oft¬Forgiving, Most Merciful. (An-Nisa 4:129)
Allah swt says in Holy Quran:
And if a woman fears cruelty or desertion on her husband's part, there is no sin on them both if they make terms of peace between themselves; and making peace is better. And human inner-selves are swayed by greed. But if you do good and keep away from evil, verily, Allâh is Ever Well¬Acquainted with what you do. (An-Nisa 4:128)
So the summary of above discussion is that a man can marry more than one woman provided that he does justice with all of them.And if he finds himself weak to do justice than he can look after only one to avoid wrath of Allah for doing injustice.
An important issue in this regard is that if one or more of the wives in polygamy surrender one or more of their rights with free will it is allowed for them.
