Yevamot 32A

ומקצתו חלוץ.

and part of it must be released by ḥalitza. That is, if two women were married to a single man, one of these women must enter into levirate marriage and the other must perform ḥalitza.

ויאמרו! אי דמייבם והדר חליץ ⁠— הכי נמי.

The Talmud wonders: So let them say it. Why would it be problematic if people thought that? Even were they to act upon this mistaken assumption it would cause no harm, as there is no transgression involved in performing ḥalitza. The Talmud answers: If he were to consummate the levirate marriage with one and then later proceed to perform ḥalitza with the other, then indeed there would be no reason for concern.

אלא גזירה דילמא חליץ ברישא והדר מייבם, וקם ליה ב״אשר לא יבנה״, ורחמנא אמר: כיון שלא בנה ⁠— שוב לא יבנה.

Rather, the requirement to perform ḥalitza with both women is a rabbinic decree that was instituted lest he first perform ḥalitza with one of his brother’s wives and subsequently consummate the levirate marriage with the other. Under such circumstances, he would in fact be violating a prohibition. Once he performs ḥalitza with the first woman he is subject to the prohibition indicated by the verse “So should it be done to the man who does not build his brother’s house” (Deuteronomy 25:9). In this verse God states that once he did not build his brother’s house but rather opted to perform ḥalitza with one of his brother’s wives, he may not proceed to build it by consummating the levirate marriage with a different wife.

אמר רבא: נתן גט למאמרו ⁠— הותרה צרתה. אבל היא אסורה, דמחלפה בבעלת גט.

Rava said: If the brother who performed levirate betrothal in the case described in the Mishnah subsequently gave a bill of divorce to that wife in order to nullify his levirate betrothal before he died, her rival wife is rendered permitted to the third brother. The third brother is allowed to consummate the levirate marriage with the wife of the second brother because this wife is no longer considered to be the rival wife of a woman with a double levirate relationship. The bill of divorce serves to nullify the act of levirate betrothal completely. However, the woman with whom the brother performed levirate betrothal and then received the bill of divorce is forbidden to the third brother. Why is this? She might be confused with a woman who receives a bill of divorce. In general cases where levirate betrothal was not performed, if a man gives a yevama a bill of divorce, he is no longer allowed to consummate the levirate marriage with her. If it were permitted to consummate the levirate marriage in this case, people might mistakenly do so in other cases of divorce as well.