In the Kaddish recited at the end of Musaf on Rosh Hashanah, the Hazan adds a special insert that begins "Te’anu Ve’te’ateru Min Ha’shamayim." In this section, the Hazan wishes the congregation many blessings, that G-d should open for us many different "gates" – such as "the gates of light," "the gates of love and brotherhood," and so on. It is customary for the congregation to respond "Amen" after each wish.
Hacham Bension Abba Shaul (Israel, 1924-1998), in Ner Siyon (listen to audio recording for precise citation), laments the fact that many people answer "Amen" to these blessings with greater emotion and enthusiasm than they express in the standard responses to Kaddish. He emphasizes that the "Te’anu Ve’te’ateru" section is a later addition to Kaddish, and must not be treated with greater importance than Kaddish itself. We need to be careful not to confuse the primary responses of "Amen" with the secondary responses. And, our Sages teach that one who answers to Kaddish with all his concentration and feeling can annul even the harshest decrees. Therefore, while it is certainly commendable to answer "Amen" to the blessings in "Te’anu Ve’te’ateru" with great fervor, we should invest that same amount of feeling and emotion into the standard responses to Kaddish.
Summary: It is customary for the congregation to recite "Amen" to each of the special blessings pronounced by the Hazan during the "Te’anu Ve’te’ateru" section added to the Kaddish at the end of Musaf on Rosh Hashanah. This is a commendable practice, but one must ensure to answer "Amen" to the standard portions of Kaddish with no less fervor and emotion as that with which he answers "Amen" to the special additional blessings.