Masechet Kiddushin (betrothal), Perek Bet, Mishnah Zayin: On a Torah level, two sisters are not allowed to marry one man, and the same is true of a mother and a daughter. Not only are these marriages forbidden, but they are not tofes (effective); they do not take effect if they try to make it happen. For example, if a man is married to a woman and then later tries to marry her daughter, the Kiddushin would not take effect. We say that any time there is a woman who is karet (punishable by excision) to a man, if he is with her, that marriage does not take effect if he tries to get engaged or married to her.
So our Mishnah is going to talk about what happens if a man tries to get engaged to a mother and a daughter, or to two sisters, simultaneously, right at the same time. The Mishnah says: If a man tries to get engaged to a woman and her daughter, giving each one a perutah (small coin) at the same moment, or to a woman and her sister at the same time, they are not engaged. Getting engaged to either woman here would make the other woman a forbidden relative, and he cannot get engaged to her. Neither engagement takes effect. Since they are both happening simultaneously, they both get knocked out, and neither takes effect right there on the spot.
Now we come to the next one. This is a story to corroborate what happened here, with a few halachic details that accompany it as well. There was once a group of five women, and among them were two sisters. Someone gathered a basket of figs. He wanted to take this whole basket and get engaged to all five women right at the same time. There were at least five perutot worth of te'enim, of figs, in this basket. The figs belonged to the woman. They grew on a tree owned by this group of women, and the man took them without permission. But it was during the Shemitah year (Sabbatical year), and therefore they were considered ownerless, and he was allowed to take them.
We can learn from here that if it was not the Shemitah year—in other words, if the figs were owned by these girls and it was a regular year, and the figs had been taken without permission—he could not use those stolen items to get engaged to them, even if they were the women's own items that had been stolen and they wanted back. He cannot use those either.
So now he is trying to get engaged to these five women; among them are two sisters. He tells them, “All of you women are engaged to me with this basket of figs.” One of the women accepts it on behalf of all of them. So we see here as well that one of the women who is becoming engaged is allowed to act as the shaliach (agent) for someone else as well, for her to get engaged as well, even though she is a tzara, even though she is now a co-wife. So she can act as a shaliach. One woman is accepting it for everybody else, for all five of them to get married.
And the Hachamim (sages) said that here we have three women who are unrelated to each other. All of them are engaged, but the two sisters are not engaged. A man cannot get married or engaged to two sisters right at the same time.