I have a 100 year old 3 story house which had a water leak on the outer edge corner of the house(supporting wall). I thought placing a I-beam across the floor joist might fix this problem. The whole corner needs to be replaced including the corner wall support. Which I don't think the corner wall support wouldn't be a issue. But, I am worried the structure of the outside load baring wall will create more problems after I level the wall, Also, creating a domino effect on the rest of the wall and house.
If you jack up your first floor joists with a beam and floor jacks, you want to do it very slowly (1/8" a day over a few weeks). Most importantly, as you jack up the joists, you also want to shim between the foundation wall and the joists (assuming the foundation wall is still sound).
If that corner of the house sags noticeably (if you can see that it sags just from looking at it), you will have to dig trenches to reach the underneath of the foundation walls, a job for which this forum's advice is not suited (call an engineer).