  We analyze an unconventional inter-subband paired phase in a 2D doped
superconductor considering both systems with the inversion symmetry and with
the inversion symmetry broken. We find that for a centro-symmetric system the
inter-subband pairing can appear in the high concentration regime when the
repulsive Coulomb interaction leads to the nearly degenerate symmetric and
antisymmetric state. We discuss in detail the mutual competition between the
intra- and inter-subband paired phase. For systems with broken inversion
symmetry, we find that the critical temperature has a characteristic domelike
shape as a function of the asymmetry parameter, which is explained as resulting
form the inter-subbband pairing. This results is discussed in the context of
the domelike shape of $T_c$ in the LaAlO$_3$/SrTiO$_3$ interface.
