When foundation raising beats shoring up what's there
If the house only needs its existing support shored up, one pier maker's guide says helical piles suit repair work. Portable equipment can set them in tight spaces, with no heavy machines near the old foundation and none of the shaking that driven piles cause. When the goal is getting the house higher, though, you're building new support. I'd rather do that properly while the house is up, because once it's back down, what's under it is hard to reach.

