Many buildings permit stairwell entry, but limit stairwell exit for fire code (1st) and security reasons (2nd). You'll want to check to see that you can exit at floor n-1 before attempting this, or you'll be riding the stairs all the way down.
I used to work in a shiny new LEED certified government building here in DC. My office was on the second floor. I had to take a elevator every day because the only stairs were for fire use. So frustrating.
