You need a workaround, there are at lest two ways to solve this:
1) Create multiple files with desired stories and Hot Link them in (not my cup of tea). But it is a perfectly reasonable approach. IF you think your levels will change frequently, this is probably your best bet. I just re-read your post; are the different floor levels tied to different units? If so this is most definitely the option to pursue.
If you have multiple levels within one unit then this is a viable option:
2) Use the View Map's ability to save views with distinct "Floor Plan Cut planes" and then place multiple views of the same story with these different cut planes onto a layout sheet.
The concept is to A) start with ordinary story 1 ,2, 3 etc. B), draw the various levels within Story 1. C), create as many story 1 plan views as you have story 1 levels. D) Change the "Floor Plan Cut Plane" in each view to 3FT (or your preference) above that level's floor elevation. E) Finally, go the layout sheet and place each level view cropped as needed next to each other to create a composite view that reflects your plan.
Also, you will be drawing walls (and other stuff) at various levels, so, set up the walls (and other stuff) as per your requirements, save a favorite and call that MyWall-L1.0, then change the base elevation of that same wall to the next level up, and save that as a favorite MyWall-L1.1 or whatever. Save favorites of all the walls, slabs, windows etc. This is a great management tool to use at any time, but crucial while working in various levels within one story. Plus when you come back to this file a couple of weeks later, you will be thankful to have all the settings saved as favorites.
Snap