Can’t build out? Build UP.
We’re working on a kitchen design for a client right now that incorporates an additional ledge of countertop surface area. It sits between the backsides of the cabinets and the wall to which they are secured.
Basically, we framed out a 40″ high wall up against the exterior wall, & it will be capped off with a piece of quartz matching the main countertop. It doesn’t have to match, necessarily; it could be stainless steel, for example.

Pros & Cons
Obviously, a plus is the additional storage surface area gained. It could be used for anything from spices to small herb growing containers to a handy book notch.
On the invisible side, the skin on the interior side of the existing wall can stay as is. Any new wiring & piping can live in the newly framed wall, just like it would in new construction. In cases where there is little or no insulation in the exterior wall, it can be added in the new one.
As for the negatives, it does gobble up 6″ of floor footprint real estate, and it adds to the cost of materials & labor. So if it is already a very narrow space, or the budget is super tight, it wouldn’t be a great option.
Outside the box
There are multiple ways to gain the extra shelf. One is to frame the additional wall described above.
Another is to use stand-off hardware & make a 5 ” or 6″ deep elevated surface. The bonus with this method is that the space under it is still usable.