The keep in a castle was, in many ways, like a block of flats. Each set of rooms was piled on the one below.
In fact, each set of rooms occupied all of the space, so the only place for the stairs was inside the walls.
It's just as well the walls were over 2m thick. To save space (as well as to be better for defence) most stairs were tight spirals. The exception might be the main stairs leading to the great hall, and one leading down to the basement and kitchens.
