The answer is yes. The Qur'an states: "Marry women of your choice, two or three or four" (4:3). Yet, despite this seemingly open invitation to polygyny, the overwhelming majority of Muslim men are content with only one wife. I often joke with my wife and say, "You know, I can always marry another." But, in all seriousness, would I ever want to take a second wife? Absolutely not.
Why? Because of the rest of verse 4:3: "Marry women of your choice, Two or three or four; but if ye fear that ye shall not be able to deal justly (with them), then only one." Leaving aside the fact that I am more than happy with the wife God has blessed me with, having more than one wife is just not worth it...assuming, of course, my wife acquiesces to my taking a second. If she does not like the idea of sharing her husband, then she has the right to ask for a divorce. In fact, a woman can stipulate in the marriage contract that her husband cannot take a second wife.
In addition, Islamic law is very stringent when it comes to justice between wives. If one has a house, the other has to have an eqivalent house. If one has a Lexus, the other must also have an equivalent Lexus. Eat dinner out with one, the husband must eat out with the other at the same or eqivalent restaurant. If he can love both equally---impossible, I know---than he must. In fact, if a judge in an Islamic court deems that a man would not treat two wives equitably, he is empowered to prevent him from marrying a second wife.
This is not to say that I am for an outright ban on polygyny. There are instances where it makes sense to take on a second wife if one is able. For instance, if a woman cannot have children, rather than dump his wife, a man can take on a second wife and have children with her. This is a common scenario in the Islamic world.
Many people are disturbed by this scenario, and I do not understand why, frankly. I find it puzzling that polygynists are condemned as "unnatural," while the cries of condemnation are not nearly as loud when married men--Bill Clinton, Chicago Tribune columnist Bob Greene, the Reverend Jesse Jackson, among others--admit to marital infidelity. The men who marry more than one wife have pledged to love and take responsibility for them and are liable to be placed in jail. Yet a married man who has 100 mistresses would not even be arrested. Something is wrong with this picture.
Nevertheless, the issue of multiple wives is a non-issue for me. God has blessed me with the best wife a man could ever have, and no woman is worth losing the wife I now have. Although I would not speak out against anyone wanting to take another wife, I would never do it myself, and I think the majority of Muslim men agree with me. They just won't tell their wives that.