amphora - I misunderstood your objective, sorry.
This is my understand of the design, exiting in red, proposed in green:
My comments on design:
1) For overturning of the retaining wall, note that the "pivot point" is on the existing pile cap. A large, slightly eccentric load applied to the pile cap. Perhaps more than the pile/cap were designed for.
2) For sliding of the retaining wall, horizontal friction applying lateral force to the pile cap. Perhaps more than the pile/cap were designed for.
3) Proposed retaining wall is partially supported by piling and partially on it's own heel slab. Never a good combination, risk of differential settlement and problems associated with it.
4) Proposed retaining wall does not have a "toe". Because of this geometry, difficult (but not impossible) to design a cantilever retaining wall that meets overturning and sliding requirements.
My comments on constructability:
1) Existing 11+ foot high wall has "failed", I assume this means structurally compromised in some manner. It's not a properly designed retaining wall, anyway. Just a "regular" wall, no surprise it has failed. Full depth excavation to construct the new wall may (and likely would) collapse the existing (failed) wall... possibly onto workers.
2) If the existing wall survives excavation and preparation of concrete placement, then the existing (failed) wall will be subjected to hydrostatic pressure from fresh concrete. Possibly collapsing the existing (failed) wall onto workers.
Suggestion: Demolish the existing (failed) wall and design/construct a replacement retaining wall (that has a toe). Far less risky and expensive.
Note: If my understanding of the drawing is wrong, of course, my comments may be wrong also.