A wife can stipulate her husband can't take a second wife, or else she'll divorce him.

But what if she doesn't make the stipulation. Can he do it without telling her? Here is depends on case by case basis.

Not to leave you handing, here's a general ruling:

Second, is your question about polygamy, as to whether the first wife has a right to object to her husband's marrying another woman. According to scholars, the Shariah does not require the husband to get the consent of the first wife for a second marriage. If the conditions for a second marriage are right according to the Shariah, he can legally go ahead and marry. But we need to understand the spirit of the Islamic ruling first.

For instance, if the second marriage is likely to upset the first marriage and the family structure already established, then a second marriage should be avoided, as it undermines the very purpose of the Islamic rules of marriage. But the permission of plural marriage is given in the context of protecting widows, as they need to be taken care of. In the very same verse it is stated clearly that if a man cannot treat his wives with equity, he should not marry more than one woman. This is a clause usually ignored or taken lightly by many men, depriving women the rights Allah Almighty has granted.

It is also worth mentioning that the bride has the right before marriage to demand her fiance to agree in advance to certain conditions of hers, in case he is interested in pursuing another marriage later on. Actually, this can be part of the marriage contract. As it is the duty of Muslims to fulfill all obligations, the Muslim husband cannot but honor such a condition.