You may notice that when you change an elements home story in the element selection settings, the elevation (height to project 0) also changes, or more accurately remains the same relative to its home story. This means that if you move a slab from the first floor to the second floor, it will move up the difference in the story settings.
Home story changed from Story 2 to Story 3 (Please ignore the sloppy 3/64″ modeling)
If, however, you need to locate an element to a new story, but maintain its relationship to project 0, so that it stays at the same elevation but is located on a new story, you will need to relink the elements home story. This is done with a simple right click function, rather than in the element settings. Simply select the elements you want to change the story settings of, right click, select Relink Home Story… and the elements will remain at the correct height/elevation, but be set to the new home story.
Right click after selecting the element to redefine the elements home story
The elements will remain in their original location