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, sallallaahu ʻalayhi wa sallam, is 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 Prophet warned saying: "It is not allowed for a man who believes in Allah 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.