Our custom is to extend the "Yeheh Shemeh Rabba" response during Kaddish all the way to "Da'amiran Be'alma." It sometimes happens that the Hazzan does not recite "Yeheh Shemeh Rabba" slow enough to allow the congregation to complete their response before he recites "De'Kudsha Berich Hu." The congregation is meant to answer "Amen" to "De'Kudsha Berich Hu," and the question thus arises as to whether they may answer if they are still in the middle of their "Yeheh Shemeh Rabba" response, having yet to reach "Da'amiran Be'alma."
The Arizal, in Sha'ar Ha'kavanot, implies that one should not respond to "De'Kudsha Berich Hu" if he is still in the middle of "Yeheh Shemeh Rabba." This is the ruling of the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Rav Pe'alim. One could explain that the "Amen" response to "De'Kudsha Berich Hu" is less significant than the other "Amen" responses to Kaddish, as evidenced by the fact that not all customs require answering "Amen" at that point. This response therefore does not justify interrupting "Yeheh Shemeh Rabba."
In truth, however, the Ben Ish Hai applied this ruling even if the Hazzan recites "Yeheh Shemeh Rabba" so fast that he reaches "Da'amiran Be'alma" before the congregation. In the Ben Ish Hai's view, even the "Amen" response to "Da'amiran Be'alma" does not justify interrupting "Yeheh Shemeh Rabba." This was the position also of Hacham Bension Abba Shaul (Jerusalem, 1924-1998). Hacham Ovadia Yosef, however, disagreed. He maintained that although one should not interrupt "Yeheh Shemeh Rabba" to respond to "De'kudsha Berich Hu," one should interrupt to respond to "Da'amiran Be'alma."
Optimally, of course, the Hazzan should recite "Yeheh Shemeh Rabba" slowly, in order to allow the congregation to complete their response before the Hazzan reaches "De'Kudsha Berich Hu." The Ben Ish Hai laments the fact that he was hardly ever able to answer "Amen" to "De'Kudsha Berich Hu," because the Hazzanim in Baghdad recited "Yeheh Shemeh Rabba" too quickly. He repeatedly asked them to recite it more slowly, but they did not. The Hazzan should preferably pause before beginning "Yeheh Shemeh Rabba," and then recite it slowly, so that the congregation can finish their response in time to answer to "De"Kudsha Berich Hu."
Summary: Hazzanim should recite "Yeheh Shemeh Rabba" in Kaddish slowly, to ensure that the congregation completes their response in time to answer "Amen" to "De"Kudsha Berich Hu." If one has yet to complete his "Yeheh Shemeh Rabba" response before the Hazzan reaches "De"Kudsha Berich Hu," he should not interrupt his response to answer "Amen." Regarding one who does not finish his "Yeheh Shemeh Rabba" response before the Hazzan reaches "Da'amiran Be'alma," different views exist among the Poskim as to whether he should interrupt his response to answer "Amen" at that point.