Exactly what it says on the tin. Has this ever happened?

Yes. It happens. They usually are indifferent or antagonistic towards the others though. If you read up on the lore of the varioys lesser daedra then you'll note some of Mehrunes Dagon's invading forces were servants of other Princes. He really only has Dremora, scamps and xivilai but not always even them. It stands to reason the orhers were loaned by his brothers and sisters.

If it suits their purposes. There were Daedroth and Spider-dra in Dagon's invasion force; either they betrayed Bal and Meph for Mehrunes, or he went around asking his unbrothers for support.