[the_af]

Exactly, fighting on the stairs is pointless.

If you are the attacking army, just wait it out. You've won the siege, and any defenders up the stairs will have to either come down or starve to death. Why risk attacking up the stairs?

[vidanay]

If you're at the bottom of the stairs, stuff the stairs full of firewood (tables, chairs, dressers, etc) and light it.

[CydeWeys]

Yeah, just burn/smoke out the defenders. If you're already in the bottom of the building it's over, just a matter of time when. You can also take the castle apart and cause it to collapse.