I usually build many structures by using the room tool, the one without walls, that gives you a 3x3 room. In case of staircases I build the stairways, where they shall be, then I look for the room, I wanted to be cut out, and recreate this room with the room tool outside of the house. I do this for every floor in the house then, and store all those rooms on the outside. Then take all the stairs, I have placed, and put them out too, they will also be stored on the outside.
If I build a basement, and the house has a foundation, I use the platform tool to recreate the room, that needs to be cut out in the first ffloor/ground floor. Here the difference to the other rooms is, that I then will place it, and sink the platform intonthe ground, until it reaches the deepest possible state (that depends on the height of the foundation). Then I paint the sides of that minus platform to my likes, and place the first stairway from the basement, so that it can cut through the ceiling.
Now I copy all the fake rooms, that I stored on the outside of the house at the positions, the opened ceilings shall be. I lace them and cut the floor out. I then look, iff any friezes from the outside like to show up on the cut out places, and delete them one by one. I place the stairs starting with the lowest one, now in the other direction thatn the one from the basement - from the higher floor to the lower, until all stairs are placed. Afterwards I place fences and railings and add - again one by one - the wall panels from the second friezes menu to cover up the borders of the open space.
This sounds more complicated, than it is but it works for me. Only important thing is, to never build anything in this space afterwards again. A finished staircase is a finished staircase. If you change anything there, it can mess up the whole thing, and you possibly have to rebuild the whole thingie again. That is, why I copy the prepared fake rooms to their spaces, where they should be. I can easily do that as often, as I need to in case, I mess things up.
I´ve made a picture tutorial for this, and as soon, as I am allowed to show pictures in the forums, I will show this tutorial here too.