It currently isn't possible to get ALL the stair runs and landings within a multistory stair. It is only possible to return the standard stair that is 'copied' up. This means that you can't tag ALL the stair runs on a multistory stair, only the first one.
A similar problem existed with number systems but was fixed in Revit 2018. It would be great if the same functionality could exist for the subelements of the multistory stair.