Yevamos, Chapter 3, Mishnah 10. The Mishnah opens: "Shnayim shekidshu shtei nashim" - two men, who are not necessarily related to one another, betrothed two women who are not necessarily related to one another. "U'vish'as knisasan la'chuppah hechlifu es shel zeh la'zeh v'shel zeh la'zeh" - after the betrothal, at the time they were brought into the chuppah the two were switched by mistake, and each one brought his fellow's wife into the chuppah and lived with her. The Mishnah therefore details the various obligations that arise from this case with regard to the chatas offering.
The Basic Liability - Eishes Ish:
"Harei eilu chayavim mishum eishes ish" - first and foremost they are liable for the prohibition of a married woman, and they must bring a chatas offering, since each of them lived with his fellow's wife - the woman whom the other man had betrothed.
The Additional Scenarios:
"Hayu achim" - if the two men are not strangers to one another but brothers, then beyond the woman being a married woman she is also his brother's wife, and this is a separate liability of kareis that requires a separate chatas offering. Although the rule is that "one prohibition does not take effect upon an existing prohibition" - that a second prohibition does not ride on top of a prohibition already in place - here we are dealing with a case of a prohibition that comes "all at once": both prohibitions came into the world at the very same moment, since at the moment of the betrothal itself she became both a married woman and a brother's wife. When a prohibition comes all at once, we say that a prohibition does take effect upon a prohibition.
"Im hayu achayos" - if, in addition to the men being brothers, the two women are also sisters to one another, there is an added liability for taking a woman together with her sister, as it says: "And a woman together with her sister you shall not take." This prohibition does not come all at once, since only at the second betrothal does the woman become his wife's sister. The reason the prohibition nevertheless takes effect is that this is an "expanded prohibition": once the prohibition of a wife's sister comes into being, all of his wife's sisters become forbidden to him, and since the prohibition spreads and includes other women, it takes effect as well upon this woman who was already forbidden to him.
"Im hayu niddos" - if the women were in a state of niddah, there is an added liability of kareis and an added chatas offering on account of niddah. Here too a prohibition takes effect upon a prohibition, but for a different reason: this is an "added prohibition." Once the woman became a niddah, a new prohibition came into being regarding her that applies even to her lawful husband, for he too is forbidden to her because of her niddah status; and since the prohibition is added and spreads even to her husband, it takes effect also upon one who is forbidden to her as a married woman and for all the other reasons.
Separating Them for Three Months:
After such an unfortunate incident, the halachah is that "mafrishin osan sheloshah chodashim" - they are not returned immediately to their lawful husbands; rather, they are separated for three months, lest she became pregnant from the forbidden relations and the child is a mamzer. The separation is meant to clarify, before she returns to her lawful husband, whether she is pregnant, and whether the child came from the forbidden relations or from her lawful husband afterward.
"Im hayu ketanos she'einan re'uyos leiled - machzir osan miyad" - if the women are minors and are not capable of bearing children, there is no room for concern, and they are returned to their husbands at once.
The Law Regarding Daughters of Kohanim:
"V'im hayu kohanos" - the daughter of a kohen normally eats Terumah in her father's house, but in this scenario she becomes forbidden to eat Terumah, since the status of a zonah has taken effect upon her. And although generally, when she is not married to a kohen and the matter occurred under duress and without her knowledge, she may marry her husband - nevertheless she becomes disqualified from the priesthood under these circumstances. And as we mentioned, if she was the wife of a kohen, she is disqualified from Terumah as well, because she became forbidden to her husband: a kohen may not marry a woman who had forbidden relations, nor may he remain married to her, even if the matter occurred under duress and without her knowledge.
In summary: In this Mishnah we learned the law of two men who betrothed two women and were switched with one another at the time of entering the chuppah: a basic liability for a married woman, upon which additional liabilities are added - a brother's wife by the rule of a "prohibition that comes all at once," a wife's sister by the rule of an "expanded prohibition," and niddah by the rule of an "added prohibition." We also examined the law of separating them for three months out of concern for mamzerus, the law regarding minors who are not capable of bearing children, who are returned immediately, and the disqualification of daughters of kohanim from Terumah and from the priesthood under these circumstances.