Double sided shear walls are not always feasible. Only the designer who evaluates the shape, size, and condition of your existing house can make that determination. The original source of this information can be found in APA Research Report 154,
Double Sided Shear Walls Can Save You Money
Double sided shear walls are useful when space for a shear wall is limited and a new shear wall is required. By using a double sided shear wall one can have 6 linear feet of foundation, install a 6 foot long shear wall on each side, achieve the strength of 12 linear feet of shear wall that normally would have take 12 linear feet of foundation.
Further on in the report it states:
“Typical failure of these walls was in compression and crushing of the lumber framing where the end studs bore against the bottom and top plates..The designer should carefully consider column buckling (snapping like a pencil) of the end framing members and bearing on the bottom plate in order to transmit these forces in compression to the foundation and in tension to hold-downs. In some cases it may be desirable to stop the plate short of these end studs and allow the end studs to bear directly upon the foundation. In light of this the designer should carefully consider column buckling of the end framing members (they can buckle and snap). This is done by carefully sizing the end framing members, reinforcing them with steel, or having the end studs bear directly on the foundation.”