If one is davening a mincha kitzarah and he knows he won’t be able to finish shmoneh esrei before they say Kaddish shulaim, may he start shmoneh esrei or do we say amen yihei shmei rabbah is udif
Essentially your question applies even when one is davening a regular shmona esrei by shacharis and mincha, and by davening a little bit longer he will miss kedusha, or by every maariv where kaddish is right after shmona esrei (as they both have the same din for this). If he started shmona esrei together with everyone else he doesn’t have an obligation to finish before the chazal gets to kaddish or kedusha, as right now he started correctly with the tzibbur.
See BIur Halacha 109-1 D:H Hanichnas who questions if it is permitted or not, however the see Aruch Hashulchan 109-5, Dinim V’hanhagos Chazon Ish 5-8, Oz Nidberu 8 – 41 and Mishne Halachos 5-27 that it is permitted, and that this is the minhag haolam. Also see Silmas Chaim 122.