  Accumulation layers with very large concentrations of electrons where many
subbands are filled became recently available due to ionic liquid and other new
methods of gating. The low temperature mobility in such layers is limited by
the surface roughness scattering. However theories of roughness scattering so
far dealt only with the small-density single subband two-dimensional electron
gas (2DEG). Here we develop a theory of roughness-scattering limited mobility
for the multisubband large concentration case. We show that with growing 2D
electron concentration $n$ the surface dimensionless conductivity
$\sigma/(2e^2/h)$ first decreases as $\propto n^{-6/5}$ and then saturates as
$\sim(da_B/\Delta^2)\gg 1$, where $d$ and $\Delta$ are the characteristic
length and height of the surface roughness, $a_B$ is the effective Bohr radius.
This means that in spite of the shrinkage of the 2DEG width and the related
increase of the scattering rate, the 2DEG remains a good metal. Thus, there is
no re-entrant metal-insulator transition at high concentrations conjectured by
Das Sarma and Hwang [PRB 89, 121413 (2014)].
