In the past, it was customary in Ashkenaz that only one person recited Kaddish. When there were several mourners who needed to say Kaddish, it became necessary to establish an order of precedence. However, today most Ashkenazim and all Sephardim follow the custom that everyone who must say Kaddish recites it together. Even if the entire congregation recites Kaddish and there is no one there to answer Amen, that does not invalidate the Kaddish. However, lechatchilah it is preferable that there be at least two people there who can respond Amen (Kaf HaChaim 55:31). When two or more people recite Kaddish, they should try to say it in unison and should therefore stand next to each other. If the synagogue is large and it is difficult for them to gather in one place, each person may recite Kaddish in his place and those around him answer Amen.
When there are two mourners who know how to lead the prayer service and both are acceptable to the congregation, it is necessary to follow an order of precedence. This is the rule: one who is in the middle of the first seven days of mourning (shivah) takes precedence over one who is in his first thirty days (sheloshim), and someone who is in his first thirty days has priority over one who is in his year of mourning. One who is commemorating a yahrtzeit is equivalent to being in the first thirty days of mourning. If there are two mourners who are equal in status, they should divide the three daily prayers between them. They can even split the Shacharit service in such a way that one recites the main part of the prayer until after Tachanun, and the other leads from Ashrei until the conclusion of the prayer service, and then the following day they switch (Bei’ur Halachah 132, Ma’amar Kaddishin).