When a person recites Kaddish, he says at several points, "Ve'imru Amen" ("And say: Amen"), urging the congregation to respond "Amen" to what he has recited. The question thus arises as to what to do when all the men in the Minyan need to recite Kaddish. If they all recite Kaddish, then, seemingly, they cannot say, "Ve'imru Amen," because there is nobody present whom they can invite to respond "Amen."
Some Poskim rule that in this situation, one or two men should volunteer not to say Kaddish, so there will be people responding to Kaddish.
Others, however, contend that the men may all recite Kaddish without concern. These Poskim point to the fact that we end the silent Amida prayer with "Oseh Shalom Bi'mromav… Ve'imru Amen" – saying, "Ve'imru Amen" even though there is nobody listening. According to the Kabbalists, when we say, "Ve'imru Amen" at the end of the silent Amida, we are speaking to the angels. This can be applied also to Kaddish. Therefore, even if there is nobody responding, it is still acceptable to recite, "Ve'imru Amen." This is the position of Rav Eliyahu Mani (Hebron, 1818-1899), cited by the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work Rav Pe'alim. However, in Ben Ish Hai (Parashat Vayehi), after mentioning this position of Rav Eliyahu Mani, the Ben Ish Hai writes that it is preferable to have at least one person refrain from reciting Kaddish so he can respond. The Kaf Ha'haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939) added that it is best to have two people refrain, as the phrase "Ve'imru Amen" is formulated in the plural form, inviting more than one person to respond.
This is, indeed, the final Halacha – that although it is acceptable for everyone in the Minyan to recite Kaddish, it is preferred that at least two people refrain from reciting Kaddish so they can respond to the others.