All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
According to the consensus of Muslim scholars, it is forbidden to marry the sister of the wife as long as the wife is alive and the marriage contract is still valid. One cannot marry his wife's sister even if he divorces his wife and she is still in her waiting period. The ruling is the same whether the wife's sister is her full-sister or from her father's side only or from her mother's side only. The evidence for this is the Saying of Allah (which means):
{Forbidden to you (for marriage) are: … and two sisters in wedlock at the same time, ….} [Quran 4:23]
In the same vein, it is not permissible for a man to marry a woman along with her paternal aunt or her maternal aunt. The Prophet said: “A woman and her paternal aunt should not be married to the same man; and similarly, a woman and her maternal aunt should not be married to the same man.” [Al-Bukhari]
Know that all the above rulings apply to the sisters by suckling relationship, and aunts for the Hadeeth of the Prophet who said: “What is forbidden by birth is made forbidden by suckling.”
However, it is permissible for one to marry the above-mentioned woman; i.e., wife's sister, aunt, etc. after the death of his wife, or after divorcing her and her waiting period ends.
Know that he cannot marry the mother of his wife even after the death or divorce of his wife.
Allah knows best.