Gemara

9b (R. Yochanan): Before Shemoneh Esreh, one must say "Hash-m Sefasai Tiftach..." Afterwards one must say "Yihyu l'Ratzon..."

(Rav Ashi): He must say it at every Tefilah. Since Chachamim enacted it to be said with Tefilah, it is like part of Tefilah.

(R. Yehudah, son of R. Shimon ben Pazi): Since David said it after 18 Tehilim, we say it after 18 Berachos.

17a: After Rava finished Shemoneh Esreh, he would say "before I was formed, I was not worthy... I am a vessel full of shame. May it be Your will that I sin no more..."

Rav Hamnuna Zuti would say this Viduy (confession) on Yom Kipur.

Mar brei d'Ravina would request "Elokai Neshamah (guard my lips)... Yihyu l'Ratzon... (may my words and thoughts be pleasing to You, my Rock and Redeemer)."

29b (R. Tanchum): If one forgot to mention Rosh Chodesh in Retzeh, and he already finished his prayer, he repeats Shemoneh Esreh.

(Rav Papa brei d'Rav Acha): This is only if he stepped back.

(Rav Nachman bar Yitzchak): This is only if he does not normally add supplications after Shemoneh Esreh. If he normally adds, he goes back to Retzeh.

Rishonim

R. Yonah (20a DH Lo): Our Gemara (29b) connotes that the custom was to say supplications after Yihyu l'Ratzon. If they said the verse after the supplications, the Gemara should have said 'this is only if he did not yet say Yihyu l'Ratzon. If he said Yihyu l'Ratzon, which is the end of everything, it is as if he stepped back.'

Gra (OC 122 DH Im): Yihyu l'Ratzon is like an extension of Tefilah, like it says on 9b.

Damesek Eliezer: If people said Yihyu l'Ratzon after supplications, even if one stepped back, before saying Yihyu l'Ratzon he would be able to return to Retzei.

R. Yonah (ibid.): Rather, they said Yihyu l'Ratzon right after Shemoneh Esre. This is better, for Chachamim enacted to say it corresponding to David, who said it (right) after finishing 18 Tehilim. If one wants to repeat it again (after his supplications), he may. It seems that Ravina said it at the end of his supplications. Perhaps he did not say this immediately after his Tefilah standing. Rather, afterwards he said this sitting. There is no Isur to say Yihyu l'Ratzon after supplications. One may add to the Berachos of Shemoneh Esreh like the theme of the Berachah. Surely Yihyu l'Ratzon is no greater than the Berachos themselves. One may add in the middle of Berachos, and all the more so before Yihyu l'Ratzon.

Mordechai (70): In Elokai Neshamah one interrupts (to answer to Kaddish or Kedushah).

Hagahos Maimoniyos (Hilchos Tefilah 10:400): After finishing Oseh Shalom, Avi ha'Ezri says that one may answer.

Beis Yosef (DH ul'Acher): Surely he does not refer to Oseh Shalom bi'Mromav. If so, what is the Chidush that he may answer?! Rather, it refers to the Berachah Sim Shalom. They used to bless Oseh ha'Shalom in place of Sim Shalom. Once he finished this Berachah, even though he did not yet say Elokai Neshamah, he may answer. Also the Mordechai says so in Sukah (754). Re'em says that if one reached Oseh Shalom, he answers with them and returns to Elokai Neshamah, for he already finished the 18 Berachos.

Rashba (7:405, cited in Beis Yosef OC 122 DH veha'Rashba): One who prays must say 18 Berachos and then Yihyu l'Ratzon, just like David said it after 18 Tehilim. The verse is part of Tefilah. Chachamim enacted to say Hash-m Sefasai... before Tefilah, and Yihyu l'Ratzon afterwards. Therefore, one may not interrupt between Tefilah and Yihyu l'Ratzon. After one said Yihyu l'Ratzon, he may say even the entire Seder (of Viduy, i.e. confession) of Yom Kipur. These supplications (afterwards) are not part of Tefilah, therefore he may interrupt and shorten them.

Poskim

Shulchan Aruch (OC 122:1): One may not interrupt between Shemoneh Esreh and Yihyu l'Ratzon to answer to Kaddish or Kedushah, because Yihyu l'Ratzon is part of Tefilah. One may interrupt between Yihyu l'Ratzon and other supplications.

Taz (1): Initially, the Shulchan Aruch connotes that one may interrupt for anything. He concluded that one interrupts like in Birkos Keri'as Shema. We must say that initially he discusses one who says supplications sporadically, therefore they are not like Shemoneh Esreh at all, so he may interrupt like he wants. The Seifa discusses one who regularly says supplications. He made this a fixed practice, so they are a little like Shemoneh Esre, therefore one interrupts like in Birkos Keri'as Shema.

Kaf ha'Chayim (1): The Mishbetzos Zahav agrees with the Taz, but the Mechaber connotes that one may interrupt between Yihyu l'Ratzon and other supplications like one interrupts in Birkos Keri'as Shema. The Levush and others say so. There are two opinions about answering Yimloch (in Kedushah) and Amen after ha'Kel ha'Kadosh and Shome'a Tefilah, so we permit these here, for it is more lenient. Further, one may answer even a Stam Amen. We forbid only Amen after Tiskabel, Yehei Shlama Rabah, Oseh Shalom and Baruch Hu u'Vaurch Shemo, which are only customs. Kitzur Shulchan Aruch says so.

Mishnah Berurah (1): One may answer even a Stam Amen, and all the more so Amen after ha'Kel ha'Kadosh or Shome'a Tefilah, and Amen Yehei Shmei Raba, Kedushah and Borchu. This Sa'if concludes that one answers like in Birkos Keri'as Shema. There, one may not answer a Stam Amen (66:3). If one normally says supplications, they are a little like Shemoneh Esre. Here, everyone says Elokai Neshamah. Therefore, one does not interrupt before it or during it to answer a Stam Amen.

Rema: This is only in a place where the custom is to say Yihyu l'Ratzon right after Tefilah. In a place where the custom is to say supplications before Yihyu l'Ratzon, he interrupts also for Kaddish or Kedushah. In these places the custom is to interrupt with Elokai Neshamah before Yihyu l'Ratzon, therefore we interrupt also for Kedushah, Kaddish and Borchu.

Taz (2): The Gemara says that "Yihyu l'Ratzon..." is like part of Tefilah. How may one say supplications beforehand and interrupt?! Even though one may add to the Berachos of Shemoneh Esreh like the theme of the Berachah, and one may add anything to Shome'a Tefilah, that is only for a need at the time. There is no source to permit adding on a fixed basis a text that Chachamim did not fix. Even in Shome'a Tefilah one may ask only what he needs then, but not a fixed text. Also, why does the Rema permit interrupting in Elokai Neshamah before Yihyu l'Ratzon, which is part of Shemoneh Esre? He (the Mechaber, in Sa'if 2) wrote that it is improper to say supplications before Yihyu l'Ratzon! Therefore, it is proper to say Yihyu l'Ratzon twice, before Elokai Neshamah and after. Since he says that one may do so, one should always do so, since we established to say Elokai Neshamah every day, and other supplications.

Mishbetzos Zahav: One cannot say that the supplications are like an addition to Sim Shalom, for one may add to Berachos only like the theme of the Berachah.

Gra (DH uvi'Mkomos): One could say that Ravina said Yihyu l'Ratzon also before his supplications, but this is difficult. In any case surely one may say supplications before Yihyu l'Ratzon. This (before Yihyu l'Ratzon) is no more stringent than (the middle of) Shome'a Tefilah!

Mishnah Berurah (2): Even if he did not yet start the supplications, a even if he normally says Yihyu l'Ratzon right after Shemoneh Esre, and he has the opportunity to answer Amen Yehei Shmei Raba or Kedushah but he does not have time to say Yihyu l'Ratzon first, he may answer. L'Chatchilah he should be careful to avoid this, for some are stringent.

Mishnah Berurah (3): It is good to say Yihyu l'Ratzon before and after supplications.

Mishnah Berurah (4): If one finished everything but he is waiting to step back due to someone else praying in back of him, he may answer any Amen. Ma'amar Mordechai says that surely, he may answer even Baruch Hu u'Vaurch Shemo.

Keser Rosh (33 and She'altos 21, in Sidur ha'Gra p.562, 534): The Gra and R. Chaim say that according to the letter of the law, one may learn while waiting to step back.

She'elas Rav (ha'Gaon R. C. Kanievsky Shlita, 2:7:18,24): While waiting one may say Tehilim (which is like Tefilah). He may not say other Divrei Torah.

Pninei Tefilah (citing ha'Gaon R. Y.S. Elyashiv Ztz"l, p.91): If one lifted his feet (this helps like stepping back), he may speak.

Kaf ha'Chayim (2): The Bach says that Chazal enacted saying Yihyu l'Ratzon after Shemoneh Esre. Any custom not to do so is mistaken, so we are not concerned for it. Many question the Rema's Heter to answer before saying Yihyu l'Ratzon. Therefore, it is best to say it first.

Shulchan Aruch (ibid.): However, if one normally says supplications after his Tefilah, if the Shali'ach Tzibur began and reached Kaddish or Kedushah, he cuts short (his supplications) and finishes. If he did not, he may interrupt the way one interrupts in the Berachah of Keri'as Shema, even in the middle.

Source: Rashba Teshuvah (1:807, cited in Beis Yosef DH u'Le'acher). This is because supplications are not as stringent as Tefilah.

Magen Avraham (2): If there is no time to step back, he says Yihyu l'Ratzon and answers immediately.

Beis Yosef (DH v'Omer): The Gemara gave the supplications that Rava and other Amora'im used to say. The world picked Elokai Netzor. One may say even the entire Seder of Yom Kipur before or after Elokai Netzor.

Gra (DH u'Mihu): After saying Yihyu l'Ratzon he is not in Tefilah, even before he stepped back. We say (29b) that after finishing his supplications, it is as if he stepped back regarding returning (to complete an omission). In any case he should shorten his supplications in order to step back first.

Mishnah Berurah (5): The Mechaber discusses one who said Yihyu l'Ratzon. He always forbids interrupting before Yihyu l'Ratzon. 'However' applies to his final words. Even though one may interrupt between Yihyu l'Ratzon and other supplications, if he can shorten thenm in order to step back, this is better, for until saying Yihyu l'Ratzon, he is standing in front of the King.

Kaf ha'Chayim (3): Even though Elokai Netzor is requests and on Shabbos we do not request, Shirei Keneses ha'Gedolah says that this refers to one's own requests. One may say a text that Chazal fixed.

Mishnah Berurah (8): One must say Yihyu l'Ratzon slowly. It helps greatly for acceptance of Tefilah. It is proper to pray every day specifically for one's income, and that Torah not depart from his mouth, and that all his descendants will be true servants of Hash-m, and there will be no Pesul in his seed, and for everything that he knows in his heart that he needs. If one does not know how to speak Leshon ha'Kodesh eloquently, he can say it in Leshon Ashkenaz, as long as it is from the depths of his heart. It is better to fix all requests for his needs after finishing Shemoneh Esreh than in Shome'a Tefilah, so if he needs to answer Kaddish or Kedushah he will be able to answer after saying Yihyu l'Ratzon according to all opinions.

Kaf ha'Chayim (4): Even though good and evil depend on man, we ask Hash-m's help (to be silent to those who curse us...)

Kaf ha'Chayim (5, citing Sefer Charedim): A Ba'al Teshuvah should say Elokai Netzor amidst tears and great crying.

Kaf ha'Chayim (8): One should not skip Aseh Lema'an Shmecha..., for through this one merits to receive the Divine Presence, nor skip saying Yihyu l'Ratzon a second time.

Shulchan Aruch (2): It is improper to say supplications before Yihyu l'Ratzon. Rather, one says Yihyu l'Ratzon right after finishing Shemoneh Esre. He may say it again after his supplications if he wants.