Another way I tried, that's actually easier and less "messy", is raise the basement level up by one full square. Then build the main floor on top.
Then do the same as before for removing ceiling/floor in a room on part of it as a separate room.
Put the stairs in.
Only thing is, this way you have dirt around the raised foundation instead of an actual raised foundation.
https://i.imgur.com/XZZE9d1.png
https://i.imgur.com/f3JQx05.png
https://i.imgur.com/pekyoGM.png
(I made sure a door and stairs to outside worked, which it did.)