I'm using Nusach Ahskenaz weekday prayers in this discussion.
Based on what I have seen in most shuls, I have seen a shaliach tzibbur switch at these locations:
Before Yishtabach - I would think that the bracha is part of Pesukei Dezimra. Wouldn't it make sense to keep the chazzan who said the opening bracha (Baruch She'amar) say the closing one and Kaddish as well. Then switch just prior to Barchu which starts the Birkat Kri'at Shema?
Before the 2nd Ashrei - This does begin a new "section", but, I'm not sure I see the reason for switching, here, specifically, vs. e.g., just before saying Tachanun. I.e., what's special about this location more than another?
When Hallel is said, I frequently see them switch to another Chazzan for only Hallel. Then the one who said the Amidah returns to say the Kaddish - Two questions - Why switch for Hallel, and why doesn't the Hallel chazzan say Kaddish?
I've occasionally seen additional switches just before Baruch She'amar, as well. However, frequently, it's form a kid (under Bar Mitzvah) to an adult. I'm not as concerned, here. Technically, I read (there's another M.Y. question about this) that a chazzan is really not needed for Psukei Dezimra, anyway. (Maybe that's part of the reason for the switch?)
Are there any other places where switching would be allowed or are they restricted to just these places?