If someone needs to say Kaddish for a parent but is intimidated to be the only one in shul saying it, is it permissible for the Chazzan to say the Mourner's Kaddish and the Rabbi's Kaddish at the same time, even if he is not in mourning? This could be useful if the mourner would like to not be the only person heard.
Anyone can say kaddish if they have at least one deceased parent, or if they have permission from their living parents. In a synagogue with no mourners, they'll usually have someone say at least one kaddish (usually the one after Aleinu). I had a teacher who lost a parent relatively early in life; years later, he was working at one yeshiva that asked him to say every mourner's kaddish, which he found difficult as it brought up memories of the first year of loss. But he was fine doing one kaddish per service.
So if there's no one saying kaddish, and the chazzan (or any person in the congregation, for that matter) lost a parent years ago (or has his parents' permission), he certainly could and likely should do so. The question here is saying it along with an uncomfortable mourner. (Keep in mind there are synagogues that give each mourner one kaddish of his own, so the mourner would be used to saying it solo! But most mourners at this point are used to a chorus -- or cacophony -- of sorts.) I think this will be the local rabbi's call (plus whoever's being asked to say kaddish) whether the mourner's comfort warrants having someone unnecessarily saying kaddish, plus any discomfort to whoever's saying it.