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In a word, yes.
The staircase would have to be designed by a structural engineer.
Incorporated in the design would be a series of steel joists (or, wood beams hung off the staircase and connected to the walls) emanating from the center of the 6 or 8 inch round center spindle of the staircase.
The outer beams would come off the spindle at 45 degree angles so that the area from below looks like a pie slice.
The beams proceed to the walls below the windows.
They would fasten approx. 2 or 3 feet below the bottom of the windows which would give you an eight foot ceiling in the sitting room assuming that the main ceiling is at 20 feet. You enter the area by coming up through the floor and stepping off the staircase at floor level.
You could enclose the new floor area with a stainless steel (wire) guardrail or stainless posts with glass inserts.
Can you picture it?