I've seen different activities done in two Nusach Ashkenaz shuls at the end of SHacahrit between 1 Elul and Shmini Atzeret.
One shul says two Mourner's Kaddish - one after the daily Psalm and another after Psalm 27.
Another says the daily Psalm, then Psalm 27 with one Kaddish at the end.
Is there any correct way, or are both acceptable? Why would there be a debate on this? Is there any support for either custom?
In principle you could say Kaddish on just a couple verses, but you don't usually see people stopping after every few lines of the daily Psalm to say Kaddish because the general rule* is to always minimize the number of times Kaddish is said. So if there is only one mourner (or multiple mourners who are going to say Kaddish together) then say one Kaddish at the end, and if there are multiple mourners who each want their own Kaddish then stick another one in the middle at a reasonable stopping point. This logic applies to any series of verses/study after which Kaddish is to be said (eg. Alenu and Shir Shel Yom and Barkhi Nafshi etc.). (See Teshuvot Ivra 1:4:3 who makes this point.)
*Keneset HaGedola OC 55, Beir Heitev OC 55 sk 1, Maaseh Rav 53, Chayei Adam 30:7, Mishna Berura 55 sk 1, Arukh HaShulchan OC 55:3, Kaf HaChayim OC 55 sk 8, Chida (Kesher Gadol 8:9, Birkei Yosef OC 132), Ben Ish Chai Vayechi 1:9, KSA Yalkut Yosef 2:264:2, Shethilei Zeithim OC 55 sk 6, Shaar HaKolel 11:29
