Is a Muslim man allowed to be married to two sisters?
No, he cannot. The following is stated in the Quran:
“Prohibited to you (for marriage) are:― your mothers, daughters, sisters, father's sisters, mother's sisters; brother's daughters, sister's daughters, foster-mothers (who gave you suck) foster-sisters; your wives' mothers; your step-daughters under your guardianship, born of your wives to whom ye have gone in,―no prohibition if ye have not gone in,― (those who have been) wives of your sons proceeding from your loins; and two sisters in wedlock at one and the same time...” (an-Nisa, 23)
According to that verse, a man cannot marry two sisters at the same time. However, if his wife dies or if he divorces his wife, then he can marry is wife’s sister. As a matter of fact, Hazrat Uthman married Ruqayya, the daughter of the Prophet and then when she died, he married Umm Kulthum, the other daughter of the Prophet.