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I worked as a labourer doing some underpinning on a large barn conversion ~20 years ago. It wasn't as involved as you might think... dig some channels underneath the wall (with a small digger), fill with concrete, repeat.
Start with a survey to work out what's gone/going wrong? They do say that if it's no longer moving then there's no longer a problem!
I would guess the original foundation design was inadequate? Or do you have soil/slope/tree issues?
Sounds muddy.