i live in philly and we run into this all the time.
Couple of solutions--- throw a level below the basement stairwell headers. ( they usually sag at the intersection of the lowest step in the basement. Get a 2 1/2 ton jack ( you can do it with a 4x4 and a fulcrum.) i suggest a jack.
Jack the header beams up, away from the intersection ( about 12 inches away) once it shows level, nail a few 2x4s to the side of the headers, this should pick up the weight, put a pressure treated 2x12 below the intersection and install a screw jack to support the load. Slowly remove the shoring studs.
You can also throw a wall below the header but your floor in the basement may not be strong enough ( smack the floor with a good shot from you hammer, if the hammer bounces back you are probably ok if it sounds hollow you are in for a pain in the butt. Do this also where the screw jack is installed or your problem will just come back. Hope this helped
also check where the side header support beam runs into the wall. It may be rotted.