Can a Woman Deny Her Husband a Second Wife in Islam?
Question

Is there any ruling that says in a marriage contract that a wife can refuse her husband a co-wife?
Praise be to Allah.Ibn Qudamah (may Allah have mercy on him) said:
“If a man married a woman on the condition that he should not make her move from her house or her city, then this condition is valid, because it was reported that the Prophet (peace and blessings of Allah be upon him) said: `The most deserving of conditions to be fulfilled are those by means of which sexual intercourse becomes permissible for you.’
If he married her on the condition that he will not marry another wife, then she has the right to leave him if he does take another wife.”
In conclusion, then, the conditions of the marriage contract are divided into three types, one of which must be adhered to, which is of benefit to the wife, such as her being able to stipulate that he cannot make her move from her house or city, or travel with him, or take another wife or a concubine. He has to adhere to these conditions, and if he does not, then she has the right to annul the marriage.” (End quote from Al-Mughni by Ibn Qudamah, vol.7, Kitab An-Nikah)
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked this question and he replied in Al-Fatawa Al-Kubra:
“Question: a man married a woman and she stipulated that he should not take another wife or make her move from her house, and that she could stay with her mother, so he married her on this basis. Does he have to adhere to this, and if he goes against these conditions, does his wife have the right to annul the marriage or not?
Answer:
Yes, these conditions and similar ones are valid according to the Madhhab of Imam Ahmad and other scholars among the Companions and the Successors of the Companions (Tabi`un), such as `Umar ibn Al-Khattab, `Amr ibn Al-`As, Shurayh Al-Qadi, Al-Awza`i and Is-haq. According to the Madhhab of Malik, the condition states that if he marries another wife, (the first wife) has the choice of what to do, and this is a valid condition. The woman has the right to leave him in this case. This is similar to the idea in the Madhhab of Imam Ahmad. The basis for this is the Hadith narrated by (Al-Bukhari and Muslim) from the Prophet (peace and blessings of Allah be upon him): `The most deserving of conditions to be fulfilled are those by means of which sexual intercourse becomes permissible for you.’ `Umar ibn Al-Khattab said: `Rights are in accordance with conditions.’ The Prophet (peace and blessings of Allah be upon him) dictated that the conditions which make sexual intercourse permissible are more deserving of fulfilment than others. This is the ruling on conditions of this nature.”
For more details, please see the following answers: 115751, 61.
And Allah knows best.