Q. It says that one should answer Yehe Shmei Rabba with all his might, so he can answer louder than the one saying kaddish, does that include the Amen also?
A. On question 1500 in regards if omein can be answered quietly, we wrote: “Shulchan Aruch (124: 12) quoting Talmud (Brochos 45a) rules that one who answers omein should not rise his voice more than the one reciting the brocho. However, Meforshim question that it seems to contradict the teaching of the Talmud (Shabbos 119b) that if one who answers omein, with all his might the gates of Gan Eden are opened for him. Horav Shlomo Miller Shlit’a explained that this follows the opinion of those who maintain that “bechol kocho” does not mean with a loud, high volume voice, but with his greatest intention. (Ritvo ibid, quotes Rabenu Yona that it actually means loud and clamorous).
Mishna Berura (ibid. 47) maintains that if one’s intention is to rouse and energize others into answering with better and stronger kavana and intent, it is permitted. (Shaarei Brochos p. 358, quotes other answers and opinions).”
Horav Shlomo Miller’s Shlit’a opinion is that indeed, one may say the omein in a tone lower than the following Yehei Shmei Rabbo.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a