First, we have not seen anything about the location or dimensions of the adjacent building(s) and the property lines. There are several possible solutions - most are very expensive and not used for smaller projects. Slurry (diaphragm) walls, secant pile walls, tangent pile walls, and jet grouting are
very expensive and not (very, very rarely) used on small jobs or jobs with small footprints. Therefore, you are left with cheaper, more common options: possibly underpinning or, if underpinning is not allowed, a very stiff drilled-in soldier pile wall, braced or tiedback as necessary.
Underpinning would not necessarily need to extend the extra 20 feet to bedrock. That would be very expensive. Design the underpinning to bear on suitable soil at or slightly below excavation subgrade. Dewatering will be very important and should be implemented prior to any underpinning or drilling for soldier beams. Soldier beam walls are considered flexible support systems. Therefore, they are often (usually?) not recommended for supporting closely adjacent buildings and underpinning is used. However, if you can't underpin, maybe because the adjacent owner will not let you on his property, you may have no reasonable option but to design an extra stiff soldier beam wall. The extra stiffness should help minimize (but probably not eliminate) movement and damage. Remember, even if you underpin the building, there may still typically be from 0 to possibly 1/2 inch (I edited "12 inches" typo) of settlement.
If the underpinning will bear on soil with much better bearing capacity than the soil under the original footings, you may not need as much bearing area and possibly spaced out underpinning piers can be used with lagging between. If the soil at the new excavation depth is similar to or worse than the original bearing soils, you will need equal or better bearing area for the underpinning. If the wall to be underpinned is a jointly owned party wall, you are allowed to underpin it but you still will need permission to install tieback anchors across the property line. For sheeting or underpinning, you may need to internally brace the support wall if the adjacent owner does not give a temporary underground easement for installing tiebacks across the property line.