Each step needs to be deeper so the total area taken up by the stairway would have to be greater. Essentially the entire stair has to be rebuilt starting from the top allowing for a 10" deep tread (plus overhang) and 7" rise. You could make it somewhat less challenging by reducing the number of winder steps from four to two, rebuild only the bottom section and add 2 treads at the bottom. This would make the stair stick out at least another 20", blocking whatever's to the left of the door where the carpet starts. Done correctly this stair would probably extend through that doorway.