I faced a similar situation in 1990 with my 52' by 30', three story,
balloon-framed barn my grandfather built in 1921. The undersized
footing had cracked and sections of the foundation had toppled over.
The central 8" by 8" posts were the main supports holding the barn
erect. To correct these problems we used braced, screw-top, post jacks
at 3' intervals under 4" by 8" by 8' beams which crossed under the
floor joists of the second floor. Sequential turning the screws first
leveled then slightly raised the second and third floors as a unit.
With the building lifted we sawed off and removed all of the first
floor walls and old posts. With the upper 2/3's of the barn lifted we
excavated, formed, and poured new footings and foundation walls around
the perimeter. When these cured we built new first floor walls using
2" by 6" studs and replaced the posts with new 8" by 8" and then set
the building down on the new plates and posts. All the jacks (over 50)
and beams were rented from an equipment rental outfit. My barn was
free-standing not dug into a hillside and the low points of its sagging
wasn't more the 12 inches in one corner so our post jacks with screw
tops could handle the task. I had 8 hydraulic bottle jacks that I was
ready to use in lifting low points but they were not needed. My use
of the term "we" in the above is not accurate in that the vast bulk of
the work was done by a talented friend of mine with an acquaintance of
his helping. Most of the job went well but for one jack kicking out
under load and cracking a bone in the helper's arm. We never computed
or learned what weight we were trying to lift but figured we would keep
adding jacks until we succeeded in lifting the building. Our first
guess at the number of jacks needed was sufficient.