I don't get too far from Atlanta. I usually discourage this due to cost, recommending instead an outside addition or a retaining wall inside the basement beyond a 1:1 influence line from the foundation. To do what you want, you will need to do pit underpinning in alternate 3' sections and if this is a rubble wall you may need to pour a slab under the wall prior to digging the pit to ensure the wall doesn't come apart. After pits are filled to within 3" of the footing drypack must be rammed into the gap to transfer the load. It's a slow, expensive option.