Yes, had some smaller birds build a nest on the porch of my rental house - wasn't bothering anyone, so I let them stay rent free. They took nearly the whole summer to raise a bunch of chicks to the point they coukd fly off.

The next summer a larger bird used the nest - but built it up in size and had a bunch of chick's that flew off in a matter of weeks.

I have no idea what kind of birds they were, but the larger did use the smaller birds nest - albeit as a base to build from, not as a complete home.