Gemara

Yevamos 50a (Mishnah - R. Gamliel): If a Yavam gave a Get to his Yevamah, a second Get does not take effect (to forbid the giver to the receiver's relatives).

Chachamim say, a Get takes effect after a Get.

All this applies when there is one Yavam, whether there is one Yevamah or two.

If he gave a Get to each Yevamah, they need Chalitzah;

All this applies to one Yavam and two Yevamos, or two Yevamim and one Yevamah.

51a - Question: Why does R. Gamliel say that a Get does not take effect after a Get, nor a Ma'amar after a Ma'amar?

Answer #1 (Rava): R. Gamliel is unsure whether or not a Get repels (Zikah), and whether or not a Ma'amar acquires;

If the first Get repelled, there is nothing left for the second Get to do. If the first Get did not repel, neither does the second!

If the first Ma'amar acquires, the second Ma'amar cannot acquire. If the first Ma'amar does not acquire, neither does the second!

Objection (Abaye - Beraisa): R. Gamliel admits that a Get takes effect after a Ma'amar, and a Ma'amar after a Get. A Get takes effect after Yibum which followed a Ma'amar, and a Ma'amar takes effect after Yibum which followed a Get.

If R. Gamliel was in doubt, when Yibum is in the middle (it should acquire if possible, i.e. if the Ma'amar did not acquire or the Get did not repel. In any case no Zikah remains after the Yibum, so) it should be like Yibum at the beginning, i.e. nothing should take effect after it!

(Mishnah): When Bi'ah is at the beginning, nothing takes effect after it.

Answer #2 (Abaye): R. Gamliel is certain that Get repels and that Ma'amar acquires. However, it was enacted that Get repels one 'side' (part of the Zikah), and Ma'amar acquires one (the 'other') side;

A second Get doesn't work, since the first Get already repelled as much as a Get can;

A second Ma'amar doesn't work, since the first already acquired as much as a Ma'amar can.

A Get after a Ma'amar takes effect, and also a Ma'amar after a Get, since one acquires (one side), and one repels (the other side).

Chachamim say that we enacted that each Yavam has a power to acquire or repel with a Ma'amar or Get (therefore, a Get after a Get or a Ma'amar after a Ma'amar takes effect).

(Beraisa): In what case did R. Gamliel say that a Get does not take effect after a Get? If two Yevamos fell to one Yavam, and he gave a Get to each (e.g. to Leah and then to Chanah);

R. Gamliel says, he does Chalitzah to Leah and he is forbidden to her relatives. He is permitted to Chanah's relatives;

Chachamim forbid him to the relatives of both of them. He does Chalitzah to one of them.

The same applies when there are two Yevamim and one Yevamah.

Question: R. Gamliel says that he does Chalitzah to Leah. This refutes Shmuel!

(Shmuel): If one does Chalitzah to Ba'alas ha'Get, her Tzarah is not exempted.

Answer: Shmuel's law is like the opinion that Yesh Zikah. R. Gamliel holds that Ein Zikah.

Inference: If R. Gamliel holds that Ein Zikah, Chachamim hold that Yesh Zikah.

(Seifa): The same applies to two Yevamim and one Yevamah.

Question: This refutes Rabah bar Rav Huna!

(Rabah bar Rav Huna): A Yevamah who did a Chalitzah Pesulah (i.e. Yibum was forbidden) must do Chalitzah with all the brothers.

Answer (and Rejection of Inference): No, Chachamim agree that Ein Zikah. They argue about a Get after a Get and a Ma'amar after a Ma'amar. (Rabah bar Rav Huna's law is like the opinion that Yesh Zikah.)

53a (Mishnah): If he gave a Get to each, (both Yevamos) Tzerichos (need) Chalitzah.

Suggestion: Our Mishnah supports Rabah, who says that a Chalitzah Pesulah must be repeated by all the brothers (and likewise, by all the Tzaros).

Rejection: No. Yevamos in this situation need Chalitzah (but one Chalitzah suffices).

Rishonim

Rif and Rosh (5:1): The Halachah follows Chachamim.

Rambam (Hilchos Yibum 5:14): A Get does not totally dispel a Yevamah. Therefore, a Get after a Get takes effect.

Rosh (3:2): If a Pasul Chalitzah is equal (to or worse than Chalitzah with a different Yavam or Yevamah), we require Chazarah (repeating Chalitzah with the brothers), and all the more so the also Tzaros must do Chalitzah. The Gemara concluded that Chalitzah of Ba'alas ha'Get is equal to that of Ba'alas ha'Ma'amar, i.e. neither exempts the other. Rashi says that either exempts the other. This is difficult, the opinion that Yesh Zikah holds that these Chalitzos are equal, and it holds that equally Pasul Chalitzos do not exempt each other!

Defense (of Rashi - Gra 170:13): Rashi (51a DH Leima) brings a proof for himself. The Gemara tried to refute Shmuel from R. Gamliel, but not from Chachamim. This is because Chachamim say that Yesh Get after Get, so the Zikah of both women is equal, so Shmuel agrees that Chalitzah of one exempts the other. Another proof is from 53a. The Gemara tried bringing supports for Shmuel. One clause said that if both received Gitin, Tzerichos Chalitzah. The Gemara suggested that this supports Rabah, who says that a Chalitzah Pesulah requires Chazarah from all the brothers. Seemingly, it more directly supports Shmuel, who says that Chalitzah Pesulah does not exempt the Tzarah! Rather, it does not support Shmuel because Shmuel's law does not apply when the Zikos are equal. However, according to Rashi Shmuel holds the opposite of Rav regarding Chalitzos that are equally Pasul. Rav requires repeating Chalitzah with every brother, but Chalitzah of one exempts the Tzarah; Shmuel says that one Chalitzah exempts the Yevamah herself, but not the Tzarah!

Poskim

Shulchan Aruch (EH 170:4): If a Yavam gave a Get to his Yevamah, and then another Get to her Tzarah, he is forbidden to both of their relatives. If two Yevamim gave Gitin to the Yevamah, both are forbidden to her relatives. If each Yavam gave a Get to a different Yevamah, each is forbidden to the relatives of the one to whom he gave.

Shulchan Aruch (5): When they come to permit her, according to the opinion that a Pasul Chalitzah needs Chazarah (to be repeated with all the brothers), when there are two Yevamim and one Yevamah she needs Chalitzah from each of them. Some say that the same applies when there is one Yavam and two Yevamos and he gave a Get to each.

Tur: Rashi disagrees in this case and says that one Chalitzah suffices.

Bach (DH u'Mah she'Chosav umi'Divrei): Rashi merely copied our text of the Gemara (51b, which says that one Chalitzah suffices), but this shows that he holds like this.

Beis Shmuel (3): Rashi did not say that Rav and Shmuel argue about whether or not Chazarah is needed. This shows that he holds that (all agree that) it is not needed.

Question (Taz 6): Why does the Tur say that it seems that Rashi disagrees? Rashi (50b DH Chalitzah) explicitly says that one Pasul Chalitzah suffices when there is one Yavam and two Yevamos!

Question (Bach, Taz): On 53b (DH Tzerichos), Rashi says that it (Pasul Chalitzah) is worse when there are two Yevamos than when there are two Yevamim (and each needs Chalitzah)!

Shulchan Aruch (ibid.): According to the opinion that Chalitzah Pesulah need not be repeated with all the brothers, even when there are two Yevamim and one Yevamah one Chalitzah suffices.

Rema: The Rosh agrees with this. The first opinion requires Chazarah when she was totally Zekukah and became Pesulah, i.e. the Zikah became weaker.