Is a person who engages in premarital sex with multiple partners considered "married" since they had "one-flesh" relationships with those partners? Are they still eligible to marry according to Scripture?
A sexual encounter by itself does not constitute marriage, according to Scripture. If a person engages in sex before marriage, the person commits the sin of fornication, while a married person who commits a sexual act with someone who is not their spouse commits adultery. Neither fornication nor adultery is equal to marriage. In fact, they are sins because they are acts conducted outside the sanctity of marriage.
The Bible defines marriage in this way:
Gen. 2:24 For this reason a man shall leave his father and his mother, and be joined to his wife; and they shall become one flesh.
According to this description, a true Biblical marriage involves three parts. First, a man must "leave" his father and mother. The Hebrew word translated leave literally means to forsake or abandon, which says a man must transfer his personal allegiance from his parents to his new bride. In the years before a man takes a wife, his strongest human commitment is to his parents. God tells us to honor our mother and father, so a unmarried man's relationship with his parents takes precedence over every other earthly relationship.
Once a man marries, however, his allegiance to his parents must become secondary to his allegiance to his wife. As a married man, he is expected to put the highest priority on his relationship with his wife, and though he still honors his parents, that honor cannot be greater than his honor for his wife. The process of leaving parents and cleaving to a wife typically includes a lifestyle change (i.e., making a new home with his wife), an authority change (i.e., assuming responsibility for his wife's spiritual direction), and a heart commitment (i.e., a recognition that this new relationship take priority over all other relationships).
When a man engages in casual sex apart from marriage (i.e., fornication), he does not intend to "leave" his father and mother by such an encounter. A "one night stand" or casual sexual relationship brings no such expectations, and even if a man expresses some degree of commitment to his sexual partner, he is unlikely to grant their relationship priority over his parental relationship. More importantly, he makes no such transfer of allegiance in his heart.
Secondly, Genesis 2 says in a true marriage the man will be "joined" to his wife. Having determined to leave his parents, the man must turn to his wife and make a commitment to her that lasts forever. The Hebrew word for "joined" means to cleave or to remain steadfast, and it describes a relationship that is inseparable. Having determined to leave his parents, the man must turn to his wife and make a commitment to her that lasts forever. Just as the physical parental relationship with a child can never cease, similarly a marriage relationship will never cease until death.
Therefore, a true marriage requires a lifelong commitment from the man to love and care for the woman in marriage, and this commitment is expressed through a marriage covenant ceremony. While the ceremony itself can vary, the purpose is always the same: to give opportunity for the couple to pledge a life-long commitment to their new relationship.
Couples who enter into a marriage covenant adopt a variety of signs and symbols to communicate their commitment to the world, including exchanging rings and vows publicly, signing legal documents, changing their names, calling each other husband and wife, etc. Taken together, these practices communicate clearly that both the man and woman acknowledge their participation in a life-long marriage covenant.
Casual sexual relationships (and even long-term sexual relationships) are not equal to marriage because they lack the necessary formality of a personal pledge and life-long commitment to marriage. The sexual relationship lacks the signs and symbols of marriage, and more importantly the couple themselves lacks the perspective that they are married. If someone asked them to describe their relationship, the couple would likely say they were "only dating" or "just friends."
Finally, a true marriage requires the couple become "one flesh." A married couple is expected to consummate the marriage through sexual intercourse (or in the case where sexual activity isn't possible, they forsake other sexual encounters). Though all sexual encounters establish "one-flesh" relationships (see 1Cor 6:16), not every one-flesh relationships is equal to marriage since the relationship lacks the other Biblical components.
In summary, a marriage relationship involves: a forsaking of parent relationships, the entering into a marriage covenant, and a sexual union where possible. If a sexual union takes place without the first two components, then the relationship is not a marriage but is sin.
Though a person who engages in sexual intercourse prior to marrying commits the sin of fornication, they are still eligible to marry. Once a person has entered into a marriage, however, they may never again seek sexual gratification outside of the marriage relationship, or else they commit adultery.
You can read more about this topic in our article on Marriage and Divorce.