I wonder if this is possible now that I actual test it in Revit. I only say this because if you try and select the Run and / or the Landing of any stair section within the Multistory stair you are not able to tab through them. You can ONLY tab through them on the first stair. This may mean they are not accessible to that level.
I further tested this by “Snooping” one of the individual stairs in the Multistory stair and when reviewing the ID’s of the stringers and landings, they match the IDs of the same elements for the primary “first” stair. Also, if you try to get “ID of selection” in Revit, it does not produce anything. I think the Subelements are only for that of the first (primary) instance of the Multistory stair.