Gemara

(Rav): If three sisters fell to Yibum to two brothers, one sister does Chalitzah with one brother, another does Chalitzah with the other brother, and the third sister needs Chalitzah from both of them.

(Rabah): Since Rav requires a sister to do Chalitzah with both, he must hold that Yesh Zikah, and the Chalitzah of the third sister is Pesulah, and a Chalitzah Pesulah requires Chazarah (the Choletzes must do Chalitzah with all the brothers).

Question: If so, the first two should also need Chazarah!

Answer: If they fell together (before any Chalitzah was done), that would be true. The case is, a sister fell and did Chalitzah with Reuven, and then her sister fell and did Chalitzah with Shimon. When the third falls, each man does Chalitzah to remove his Zikah to her.

(Shmuel): One brother may do Chalitzah to all of them.

Opinion #1: Shmuel means that one does Chalitzah to the first and third. Since this is the majority, he calls it 'all of them'.

Opinion #2: Shmuel requires proper Chalitzah only to exempt the Tzarah, but the Choletzes herself is exempted in any case;

(Shmuel): (When sisters with Tzaros fell to one brother), if he did Chalitzah to the sisters, the Tzaros are not exempted. If he did Chalitzah to the Tzaros, the sisters are exempted.

27b - Question: Which is better, Chalitzah of Ba'alas ha'Get (a Yevamah who received a Get) or of Ba'alas ha'Ma'amar?

Perhaps (Chalitzah of) Ba'alas ha'Get is better, since she started being cast off;

Or, perhaps Ba'alas ha'Ma'amar is better, since she is closer to doing Yibum!

Answer (Rav Ashi - Mishnah): R. Gamliel agrees that a Get takes effect after a Ma'amar, and a Ma'amar after a Get.

If a Get were more potent, a Ma'amar would not take effect after it;

If a Ma'amar were more potent, a Get would not take effect after it!

Conclusion: We must say that they are equal.

51a (Beraisa - R. Gamliel): If two Yevamos fall to one Yavam and he gave a Get to each or a Ma'amar to each, he does Chalitzah to the first one to whom he gave a Get or Ma'amar;

Chachamim say, he does Chalitzah to one of them.

Question: R. Gamliel refutes Shmuel, who says that Chalitzah of Ba'alas ha'Get does not exempt her Tzarah!

Answer: Shmuel said his law according to the opinion that Yesh Zikah. R. Gamliel holds that Ein 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

Rambam (Hilchos Yibum 5:10): A proper Chalitzah is one not preceded by anything else. An inferior Chalitzah is one preceded by a Get or Ma'amar.

Rambam (12): If Leah did an inferior Chalitzah, she is permitted to marry a stranger, but her Tzarah is forbidden until she does Chalitzah, or until all the brothers do Chalitzah to Leah.

Question (Magid Mishneh): If Reuven gave a Get or Ma'amar to Leah and then Shimon had Bi'ah with her, she is more disqualified from Yibum than Rachel (to whom nothing was done). Still, the Rambam holds that Chalitzah of Rachel, even though it is better than Chalitzah of Leah, does not exempt Leah. This is unlike Shmuel, who says that Chalitzah of the Tzarah exempts Ba'alas ha'Get or Ba'alas ha'Ma'amar.

Answer (Lechem Mishneh): The Magid Mishneh understands that the Rambam says that whenever Yibum is forbidden, Chalitzah is inferior and it does not exempt the Tzarah. This caused his difficulties here and in Halachah 7:10. The Tur disagrees. The Rambam says that inferior Chalitzah does not exempt the Tzarah, i.e. if it is inferior to Chalitzah of the Tzarah. The Rambam relied on what he wrote below (7:9), that Chalitzah to the Tzaros exempts the sisters. The Rashba explains that when two Chalitzos are equal, one exempts the other. The Ramban says that if they are equally Pasul neither exempts the other, but a superior Chalitzah exempt an inferior one.

Rambam (7:9): If two sisters, each with a Tzarah, fell to Levi, if he did Chalitzah to the Tzaros, the sisters are exempted. If he did Chalitzah to the sisters, the Tzaros are not exempted.

Rambam (10): It seems that the same applies when Leah and Chanah fell from one brother, and Leah was a Shniyah to Levi or Chayavei Lavin. If he did Chalitzah to Leah, Chanah is not exempted. If he did Chalitzah to Chanah, Leah is exempted.

Question (Magid Mishneh): This seems correct. Just like the Isur mid'Rabanan of Achos Zekukaso makes a Chalitzah Pesulah, the same applies to any Isur mid'Rabanan. However, BaHaG says that one may do Chalitzah to the Shniyos. Some explain that only an Isur Zikah makes Chalitzah Pesulah. This is unreasonable. However, a Tosefta (6:5) supports it. The Rambam must hold that since we did not challenge Shmuel from the Tosefta, we do not rely on it. A Beraisa (20b) teaches that Chalitzah of Chayavei Lavin or Shniyos exempts the Tzarah. We must say that it is when the Tzarah is also a Shniyah or Chayavei Lavin. However, the Rambam holds that Chalitzah Pesulah does not exempt a similar Tzarah. It is not clear how to answer for the Rambam.

Answer (Gra EH 170:45): The Beraisa is like the opinion that Ein Zikah.

(Rosh 3:2): We say that Chalitzah Pesulah requires Chazarah, and all the more so the Tzaros must also do Chalitzah, only when the Chalitzah done is equal (to or worse than Chalitzah with a different Yavam or Yevamah). If the Chalitzah done was better, even though Yibum was forbidden, there is no need for Chazarah. E.g. Chalitzah of the Tzaros exempts the sisters. The Gemara concluded that Chalitzah of Ba'alas ha'Get is equal to that of Ba'alas ha'Ma'amar. Rashi says that either exempts the other. This is difficult, for this is like the opinion that Yesh Zikah, and this opinion holds that equally Pasul Chalitzos do not exempt each other. Rather, they are equal, so neither exempts the other.

Defense (of Rashi - Gra 170:13): Rashi explains according to Shmuel, unlike the version that says that if he started with sisters he may not finish with Tzaros. 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 170:5): According to the opinion that Chalitzah Pesulah requires Chazarah, Ba'alas ha'Get she needs Chalitzah from each brother.

Taz (7) and Beis Shmuel (4): The Terumas ha'Deshen (225) says that Chalitzah of a minor is totally invalid, so it does not require Chazarah. When she matures one Chalitzah suffices. We learn that any Chalitzah that is invalid mid'Oraisa, e.g. the Yavam was a minor or tricked, does not weaken Zikah, so Chazarah is not needed.

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. If the Chalitzah was Pesulah from the beginning, Chazarah is not needed.

Gra (15): The following are cases of weakened Zikah: Achos Zekukaso (she is like Achos Ishto), Achos Chalutzaso (she is like Achos Gerushaso), Ba'alas ha'Get and Ba'alas ha'Ma'amar (it is as if Yibum was done and there is no Zikah).

Shulchan Aruch (17): If an adult gave a Ma'amar or Get to Leah, Chalitzah of Leah does not exempt her Tzarah, but Chalitzah of the Tzarah totally exempts (the Zikah of Leah). If he gave a Ma'amar to one and a Get to the other, he does Chalitzah to whichever he wants and exempts both.

Beis Yosef (DH u'Mah she'Chosav v'Im): The Gemara concluded that Ba'alas ha'Get and Ba'alas ha'Ma'amar are equal. The Rosh holds like Rashi, who says that Chalitzah of either exempts the other. The Ri explains that Chalitzah of either does not exempt the other.

Shulchan Aruch (18): If two Yevamos fell from one brother, and Leah was a Shniyah to Levi, he (exempts both even if he) does Chalitzah to Leah. Some say that Chalitzah of Leah does not exempt the Tzarah, but Chalitzah of the Tzarah exempts Leah.

Question (Gra 45): The latter opinion calls this Chalitzah Pesulah. If so, also the Bi'ah is Pesulah, but the Shulchan Aruch (174:1) rules that Bi'ah exempts the Tzarah!

Shulchan Aruch (174:1): If Leah was forbidden to her Yavam by a Lav, Aseh or Shniyos mid'Rabanan, her Chalitzah does not exempt her Tzarah, but Chalitzah of the Tzarah exempts Leah.