OK guys, look here. Lets take this one "step" at a time.
1) You have an existing floor/subfloor on the second story with a "stone" staircase. How is the transition made now? Is there a wood nosing that is flush to the existing floor and overhangs a stone riser? I'm trying to get a picture of this wood to stone transition.
2) IF there is a wood nosing, you simply cut it back flush to the stone riser OR remove it and install some wood of the same thickness that DOES NOT overhang the riser.
3) Now, at this point, you can:
a) install some plywood to strengthen the existing subfloor and then
install your new flooring paralell to the existing flooring OR;
b) install new flooring running perpendicular or diagonally to existing
wood floor/subfloor
4) At the staircase/step transition, you simply install a new stair nosing that sits on top of the existing floor and is FLUSH with the new floor and overhangs the riser. Quite simple really.
Now if the issue is that the rise at this transition will be too great, then there is NOTHING that can be done EXCEPT to remove the existing flooring OR rebuild the stairs.
5) If, at the top of the stairs, there is now some sort of stone nosing, you can either attempt to remove it and re-install it at the new level OR have another one fabricated.
The only "code" issue would be the rise from the last stone step up to the wood floor on the second level. Since I don't know what the actual measurements are, I don't know if there would, in fact, be any code violation. Assuming that the rise NOW is exactly the same from the bottom step to the top, the ONLY way he could add a new floor without removing the existing floor and still be within stair code is to install a 3/8" thick floor OR thinner (5/16") and not use any plywood underlayment. You may have up to a 3/8" variance on the rise.
OK, school's over. Now go out and play!