Selecting an existing display I want to copy for a 2nd floor and dragging down it becomes a new one with a (2) appended. Ideal!! Now we just need to scroll across and associate the (2) with the Display 'Set' (2) and unassociate the original with the (2) set. Ok your way out and then draw a stair in a (Presentation) display. Editing the style you should only see one set to alter (it's the bolded one). (2) should not be bold. Now change your display set to a (2) and again edit the stair style. If you made your changes correctly, you should be now editing a newly created display rep for the stair for the 2nd floor and whatever changes you make will only appear for the 2nd floor. Now this makes it easy to set up a stair for ground floor showing the stairs going up and for the 2nd floor display with the stair going down! Or however you like it to show!! The final display changes can be done in the environment you are familiar with through working the style from the stair itself. See these 2 images.
Viewports (update) will need to be adjusted for each level displayed. It's seems that if you have not changed a viewports display rep then it will be whatever your current model space is set to. However if you specifically change the display rep inside a viewport, it will stay that way and not automatically alter (no idea what variable that is). So if you are setting up a viewport for your 2nd floor, double click inside the viewport and change the setting to Medium Detail(2) or whichever you need. Then also change the Elevation setting and you are done. If I use a previous job as my template these are already set though the 2nd floor level may be a little differerent height and may need to be altered. - easy!
Stairs another way (PN & X-ref's).(update)