Q. I have seen different minhagim with regard to saying kaddish in shul. Specifically, if there is no person saying kaddish yasom after aleinu, should a person who has previously been an avel say kaddish or should it not be said at all? Also if so, should he say multiple kaddishim, e.g. again after shir shel yom, or is one after aleinu sufficient? Also, if no rav or avel is there to say kaddish drabanan, who is qualified as a rav to say that kaddish?
Thank you very much!

A. Beis Yosef and Levush (O.H. 55) rule that one should recite no less than seven kaddeishim every day. They do not count the kaddish after aleinu in shacharis as one of them. Conversely, Mishna Berura (55: 5) considers that kaddish as one of the seven obligatory ones. Aruch Hashulchan (55: 4) maintains that one should try to answer at least ten kadeishim a day, while Igrois Hakodesh tells that he was careful to recite sixteen kadeishim daily. However Mishna Berura (55: 1) asserts that one should abstain from reciting unnecessary kadeishem, as he would be careful not to say redundant brochos.
Remah (O.H. 132: 2) rules that if there are no avelim present, the kaddish after aleinu, should be recited preferably by someone who has lost his parents. It is recited for the merit of all departed (Mate Efraim 4: 63, Nitei Gavriel 44: 19) or to sanctify publically Hashem’s holy name at the end of the tefila (Mekor Chaim 132). There is no need or benefit for a rov to recite kaddish derabbanan, as the substitute of a layman.
Horav Shlomo Miller’s Shlit”a opinion is to just recite one single kaddish at the end of davening.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a