Yevamot 29B

ואי סלקא דעתך מאמר לבית שמאי קונה קנין גמור: זה יעשה מאמר ויקנה, וזה יעשה מאמר ויקנה.

And if it enters your mind that according to Beit Shammai levirate betrothal acquires the woman as a full-fledged acquisition, then this matter could potentially have been resolved ab initio: This brother should perform levirate betrothal and acquire one sister, and that brother should perform levirate betrothal and acquire the other sister. As there is no prohibition whatsoever involved in performing levirate betrothal, the concern for violating a prohibition by consummating the levirate marriage with a sister of a woman with whom he has a levirate bond is avoided; he only betroths her, but does not have sex with her. After the betrothal, the levirate bond of her sister is dissolved and he can freely consummate the levirate marriage with her.

אלא מאי? דוחה דחייה גמורה ⁠— זה יעשה מאמר וידחה, וזה יעשה מאמר וידחה.

The Talmud objects: Rather, what then? If levirate betrothal does not serve to fully acquire the woman, what is the alternative? It must be that according to Beit Shammai levirate betrothal precludes the rival wife from entering levirate marriage with a complete preclusion. If so, there is an additional potential scenario: This one should perform levirate betrothal with one sister and preclude the second sister from entering levirate marriage, and that one should perform levirate betrothal with the second sister and preclude the first sister from entering levirate marriage. In this way, the yevamin can consummate the levirate marriage with the sisters ab initio as well. Yet the Mishnah does not allow for this possibility.

אלא מאי אית לך למימר: מאמר דהתירא ⁠— דחי, דאיסורא ⁠— לא דחי, הכי נמי מאמר, אפילו למאן דאמר מאמר קונה קנין גמור: מאמר דהתירא קני, דאיסורא לא קני.

Rather, what have you to say? One must assert that levirate betrothal performed in circumstances where it is permitted to perform levirate marriage, i.e. where there is no prohibition with regard to the close relative of a woman with whom the yavam has a levirate bond, completely precludes the rival wife from entering levirate marriage. However, levirate betrothal performed in circumstances where it is forbidden to perform levirate marriage, does not preclude entering levirate marriage. Therefore, in the case of two sisters who happen simultaneously before two brothers for levirate marriage, the sisters cannot be precluded from entering levirate marriage via levirate betrothal. So too here, with regard to levirate betrothal performed by the third brother, the same distinction can be made. Even according to the one who said that levirate betrothal acquires a woman as a full-fledged acquisition, just like marriage, there is the following difference: Levirate betrothal under permitted circumstances acquires the woman, but levirate betrothal under forbidden circumstances does not acquire the woman. Therefore, there is no proof as to the nature of levirate betrothal according to the opinion of Beit Shammai from the first Mishnah in the chapter.