Staircase Opening

Job ID: 38594528

Budget: $30 – $250 USD

Looking to create a staircase opening by cutting 4 ft of the 6 joists and attaching the mono stringer staircase to the 2x12 joist
Possibly attach a sistered 2x12 to the I beam ( no support column ) which will run 120 inches to the sistered joist of the staircase ( there should be a column support at that connection )
See photos for more detail
Must have a structural Engeneer license(seal) and insurance for NYC!