Is polygamy allowed in Islam and to what extent
Islam "allows" (but does not encourage) Muslim men to marry up to 4 wives at the same time, provided that the man is fair in treating his wives. The Quran says that if a men cannot meet this condition, then he should be married to only one woman. On the other hand, Muslim women are not allowed to be married to more than one man at the same time. Please note that "group" marital relationship is not allowed.
On a worldwide basis, most Muslim men do not marry more than one woman. The popularity of Islamic polygamy varies from countries to another. In some countries, it is more common than in other Islamic countries. For example, in Saudi Arabia, Islamic polygamy is much more common than in Egypt.
Generally speaking, Shia Muslim are more likely to practice polygamy. In Lebanon and Iraq, for example, Islamic polygamy is far more practiced among Shia Muslims than among Sunni Muslims.
The Wisdom of Islamic Polygamy