For what prayer responses (e.g. amen, baruch Hu uvaruch Sh'mo, y'he Sh'me...) may one interrupt his own recital of birkas hamazon?
See discussion here.
Summary: According to Ben Ish Chai (Chukat, 3), it is forbidden to make any interruptions during Birkat Hamazon – even to respond to Kaddish, Kedusha or Barechu. One may not even gesture or motion to somebody, such as by snapping, during Birkat Hamazon. However, during the “Harahaman” section after the main obligation of Birkat Hamazon is finished, one should interrupt to answer “Amen” to a Beracha or respond to Kaddish, Kedusha or Barechu.
There is a dichotomy regarding interruptions in bentching:
The Rema in O.C. 183:7 recommends finishing the bracha prior to the leader so that one may answer amen and refers to the laws of birchos krias shema in O.C. 53. We can extrapolate from here to other devarim shebekedusha.
However, in 183:8, the Shulchan Aruch brings an opinion (with no one arguing) that regarding greetings, we compare bentching to tefilah.
Summary: divrei kedusha like shema, greetings like shmona esre.
But, apparent from Jake, Ben Ish Chai argues.