Praise be to Allaah.
It is not permissible to marry them at the same time, because they are sisters, regardless of whether they share the same father and mother, or they have only one parent in common, because of the aayah (interpretation of the meaning):
“Forbidden to you (for marriage) are: … two sisters in wedlock at the same time, except for what has already passed” [al-Nisaa’ 4:23]
It was reported from Abu Hurayrah that the Messenger of Allaah (peace and blessings of Allaah be upon him) forbade marrying a woman then her paternal aunt, or a paternal aunt then her brother’s daughter, a woman then her maternal aunt, or a maternal aunt then her sister’s daughter, or an older sister then the younger sister, or a younger sister then the older sister.” (Narrated by al-Tirmidhi, no. 1045; Abu Dawood, no. 1768. Al-Tirmidhi said, it is hasan saheeh).
Fayrooz al-Daylami said: I came to the Prophet (peace and blessings of Allaah be upon him) and said: O Messenger of Allaah, I have become Muslim and I am married to two sisters. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Choose whichever of them you want [i.e., and divorce the other].” (Narrated by al-Tirmidhi, 1048; Abu Dawood, 1915, et al.)
Sheikh Muhammed Salih Al-Munajjid