I not long ago undertook to say Kaddish for the full year for a cousin of mine who died childless.
I also have undertaken (for many years already) to say Kaddish for grandparents and an uncle who also has no one to say Kaddish for them on their Yahrzeit.
So this year I have a problem when these clash, like next Shabbes it is my late grandmother’s Yahrzeit and I have the daily obligation I undertook on behalf of my cousin. Obviously on my late parents Yahrzeit where I am a Chiyuv on all acccounts I get someone else to say Kaddish for my cousin. What is the correct thing to do in the case of a clash like I have coming up next Shabbes?
You should say one Kaddish on behalf of both people.
A number of poskim mention that this is fine (see Ha-Elef Lecha Shlomo, Orach Chaim 61; Noda Bi-Yehuda, Tinyana, Orach Chaim 8).