Jerusalem Talmud Yevamot 3:5

משנה: שְׁלֹשָׁה אַחִין שְׁנַיִם מֵהֶן נְשׂוּאִים שְׁתֵּי אֲחָיוֹת וְאֶחָד נָשׂוּי נָכְרִית. מֵת אֶחָד מִבַּעֲלֵי אֲחָיוֹת וְכָנַס הַנָּשׂוּי נָכְרִית אֶת אִשְׁתּוֹ וָמֵת. שְׁנִייָה יוֹצִיא מִשּׁוּם אֲחוֹת אִשְׁתּוֹ וְרִאשׁוֹנָה מִשּׁוּם צָרָתָהּ. עָשָׂה בָהּ מַאֲמָר וָמֵת נָכְרִית חוֹלֶצֶת וְלֹא מִתְייַבֶּמֶת. MISHNAH: Of three brothers, two are married to two sisters and one to an unrelated woman. One of the sisters’ husbands died, the husband of the unrelated married his widow, and died. [The dead brother’s] second [wife] leaves as his wife’s sister, the first one as her co-wife. If he had “bespoken” her, the unrelated woman performs ḥalîṣah but cannot have levirate.

הלכה: שְׁלֹשָׁה אַחִין שְׁנַיִם מֵהֶן נְשׂוּאִין לִשְׁתֵּי אֲחָיוֹת כול׳. בֵּין רַבָּנִין בֵּין רִבִּי שִׁמְעוֹן מוֹדִין בָּהּ. כְּרַבָּנִין צַד שֶׁקָּנָה מַאֲמָר כְּנֶגְדָּהּ אָסוּר בַּצָּרָה. וְצַד שֶׁלֹּא קָנָה בָהּ מַאֲמָר כְּנֶגְדּוֹ אָסוּר בַּצָּרָה. לְפִיכָךְ חוֹלֶצֶת וְלֹא מִתְייַבֶּמֶת. כְּרִבִּי שִׁמְעוֹן קָנָה מַאֲמָר שְׁתֵּיהֶן מוּתָּרוֹת. לֹא קָנָה מַאֲמָר הָרִאשׁוֹנָה אֲסוּרָה וְהַשְּׁנִיָּה מוּתֶּרֶת מִסָּפֵק חוֹלֶצֶת וְלֹא מִתְייַבֶּמֶת. HALAKHAH: “Of three brothers, two are married to two sisters,” etc. Both the rabbis and Rebbi Simeon will agree in this case. For the rabbis, the part of the co-wife parallel to that which “bespeaking” acquired [in the widow] is forbidden. Also, the part of the co-wife parallel to that which “bespeaking” did not acquire [in the widow] is [still] forbidden¹⁰⁶Since no woman can be the wife of two men; since she cannot have partial levirate, she cannot have levirate at all.
In this Mishnah and the next, the only question is why the unrelated woman has to perform ḥalîṣah. These Mishnaiot require the third brother to be married.. Therefore, she performs ḥalîṣah but cannot have levirate. Following Rebbi Simeon, if “bespeaking” acquires, both are permitted¹⁰⁷To marry outside the family without formalities.. If “bespeaking” does not acquire, the first is forbidden but the second permitted. Because of the doubt, she¹⁰⁸The first, unrelated, wife is forbidden for outsiders without ḥalîṣah. {The Mishnah in the Babli switches the places of “first” and “second” in the Mishnah; students of the Babli consider this paragraph corrupt.} performs ḥalîṣah but cannot have levirate.