Watch this video from This Old House to learn how add stairway headroom.
1 Carefully pry old stair treads from staircase.
2 Use reciprocating saw to cut out the old stair stringers.
3 Cut new notched stringers from 2x12s using a circular saw; finish cuts with handsaw.
4 Attach metal hanger plates to top of each stringer.
5 Nail metal timber hangers to bottom of each stringer.
6 Set new stringers into stairway opening.
7 Fasten top of stringers by nailing through hanger plates and into header.
8 Secure bottom end of stringers by nailing through the timber hangers.
9 Nail new risers to stringers.
10 Rip old treads down to fit new stringers.
11 Nail the stair treads to the stringers.