A recent mean velocity transformation (Trettel and Larsson 2016) converts compressible mean velocities into equivalent incompressible mean velocities. This transformation works properly for channel flows but does not work properly for boundary layers. A two-dimensional extension of this transformation reveals the inherent limitations in the transformation as an extension of the incompressible law-of-the-wall. The transformation cannot properly transform the outer layer coordinate in boundary layers, and the error associated with this correlates highly with the error in the transformation itself. Despite these limitations, the two-dimensional extension reveals additional scaling laws for compressible wall turbulence, including scalings for the streamwise coordinate and production rates.