Fathwa, - Polyandry in Islam

Question
According to Islam women cannot marry more than one male as then we
will not know who the father is. But today we can know who the father
is by DNA testing. So how can we answer this question if posed by a
non-Muslim?
Answer
All perfect praise be to Allaah, The Lord of the Worlds. I testify
that there is none worthy of worship except Allaah, and that
Muhammadis His slave and Messenger.
You have to know that Islam prohibits a woman to marry more than one
man, this is not just to protect the progeny, but for many other
wisdoms. These wisdoms are known by some people and not known by
others. Therefore even if it is confirmed that the father of the child
can be determined by DNA testing, still this does not change the
ruling due to several reasons. If the woman is busy taking care of
more than one husband, which one would she obey, taking into
consideration that people differ in their nature and character? One
wants to travel and the other wants to stay where he resides, one
wants to have sexual intercourse with her at a specific hour, and the
other wants the same at the same time. One wants hot food and the
other wants it cold, and other unlimited matters. So how can life be
acceptable with the above conditions? In addition to this, she has to
fulfill the need of her husbands whether in relation to sexual
intercourse or else. If we assume that their needs are at the same
time, how can she fulfill them? If she is impregnated by one husband
and then others have sexual intercourse with her, then they have
committed the prohibition, from which the Prophetwarned saying: "It is
not allowed for a man who believes in Allaah and the Last Day, to have
an intercourse with a woman who is pregnant from another man." ]Ahmad
and Abu-Daawood[
In addition to the above, if the woman has many husbands, it is not
safe for fatal disease to spread, like AIDS and other diseases.
Allaah knows best.