Is it possible in Dwarf Fortress to add floor constructions without having to move furniture that is already occupying the same space? How should I do that?
No, if you've already built furniture you can't then build a floor tile underneath it.
You'll need to dismantle the furniture first, build the floor, then rebuild the furniture. Also don't bother engraving the stone first if you're going to floor over it, building a floor (or furniture) over an engraving destroys the engraving, which can lead to unhappy thoughts if you accidentally deface someone's masterwork.
On the other hand, smoothing out the stone beforehand is useful as free practice for your engravers.