Interesting that nobody has answered yet
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Since Chaos Daemons are a manifestation of a small part of their parent god they can't change their allegiance. They are bound to their parent god and use his energy.
That being said I could see a Tzeentchdaemon (like the Changeling) hiding as a daemon from another god.
The question is of course howmuch can daemons be affected by the powers of the other gods? Can Nurgle make Khornes brass rust? Can he infect a Horror? Can Daemonettes seduce a Blood letter? Could be yes to all (well, I don't think any daemon can be seduced, actually), but in every case the Daemons wouldn't switch sides.
It's something different with mortal followers of the gods (and Daemon Princes to some degree). They can actually switch sides. In the Lords of Silence-novel there seems to be a plague marine who seems doubtful if he chose the right god and seems to wonder if he should have become a Khorne follower instead.