Any Muslim who marries a woman is prohibited to marry her sister at the same time based on the general evidence prohibiting this. Allah states:
Forbidden to you (for marriage) are: your mothers
...and two sisters in wedlock at the same time, except for what has already passed
Ibn Al-Mundhir said that Muslim scholars unanimously agreed on the prohibition of
marrying two sisters at the same time. Consequently, it is not permissible for you to marry your wife's sister until after you have divorced your wife and she has finished her `Iddah (woman's prescribed waiting period after divorce or widowhood). After that, it is permissible for you to marry the sister and you are no longer Mahram to your ex-wife. It will not be lawful for you to look at her or be alone with her and she will have to cover up in your presence. If you wish to divorce your wife, it is necessary to announce the divorce, whether by official papers or by proclaiming it among people and have witnesses, to ensure (Part No. 18; Page No. 239) the rulings and rights guaranteed by Shari`ah (Islamic law). Your wife must be notified that she has been divorced in order that she will know her rights and obligations and deal with you as a non-Mahram, covering up in your presence, never remaining alone with you and treating you accordingly. Out of your kindness you should treat her well, provide for her, and help her in her affairs as the mother of your children and your ex-wife, and you will be rewarded by Allah, in sha’a-Allah (if Allah wills). May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.