We have heard the term, cupola. Right?
I think that definition may not allow for a floor but don't really know. I used to live next to a little house that had what we called a cupola at the top of the stairs to the attic. The son in the family used that as a bedroom but it was on that little house long before he was born. It looked rather odd on such a small house.
@buckabucka , yours fits better on a large, fully 2-story home.
@Ridgerunner 's idea reminds me of the oldest building on the college campus where I went to school. Some graduate students had offices on the top floor, 4 stories. I wasn't one of them but if my buddy was in his office, I could show up, walk into his tiny closet ... and climb the ladder through the trapdoor in the closet ceiling - flipping a light switch on my way

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I'd emerge in the attic, continue on a walkway above the ceiling joists to another ladder. Through another trapdoor, I arrived on a platform surrounded by ornamental guard rail in the center of the roof.
Since that old building was on the highest hill on campus, I could see for miles! It was a great place to read a book on a warm spring day

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Steve