It depends upon how you drew the staircase, If it is a component or group, open it for editing and select all of the geometry. Then get Scale and do the scaling operation. This won't have any effect on the material scaling.
If you drew the treads and risers as components separate from the stringers, You won't want to scale the entire staircase anyway. This would change the thickness of the stringers. In that case you would want to Move a stringer and then adjust the tread and riser components separately. You could open the components and use Scale, Move or possibly Push/Pull for that. None of those modifications would affect the material.
I think this is a common issue for folks because they can scale a group or component without opening it for editing. There are some applications for that but more often, it is the geometry that should be getting scaled.