A capping apparatus for covering a pre-existing stair structure can include: a tread element; and a trim piece attached to the tread element proximate a longitudinal edge of the tread element. The trim piece includes a back surface defining: a first recess for receiving a thick sub-tread for a first type of pre-existing stair structure; and a second recess for receiving a thin sub-tread for a second type of pre-existing stair structure. Methods of manufacturing and installing the capping apparatus are described.