  We consider Kohn-Luttinger mechanism for superconductivity in a
two-dimensional electron gas confined to a narrow well between two metallic
planes with two occupied subbands with Fermi momenta $k_{FL} > k_{FS}$. On the
basis of a perturbative analysis, we conclude that non-s-wave superconductivity
emerges even when the bands are parabolic. We analyze the conditions that
maximize $T_c$ as a function of the distance to the metallic planes, the ratio
$k_{FL}/k_{FS}$, and $r_s$, which measures the strength of Coulomb
correlations. The largest attraction is in p-wave and d-wave channels, of which
p-wave is typically the strongest. For $r_s = O(1)$ we estimate that the
dimensionless coupling $\lambda \approx 10^{-1}$, but it likely continues
increasing for larger $r_s$ (where we lose theoretical control).
