So-called nussach Ashk'naz ends the weekday shacharit service with kaddish yatom, the psalm for the day, (seasonal insertions if applicable), and kaddish yatom again. Elbogen is silent on it. Why is this done?
The Beis Yosef in Orach Chaim 55 says that we should say a minimum of 7 Kadishes a day from the Posuk in Tehilim 119 "Sheva Bayom Hillalticho". Over the years as there has been times that Shacharis started without a Minyan there was a need for an extra Kaddish at the end. This has led to some Shuls saying a seperate Kadish Yasom after Aleinu and another one after the Yom. Many Yeshivos do not say it twice as they say it at the beginning of Davening.