  We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the
bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the
two-leg ladder model with diagonal hoppings, studied previously by the present
authors, superconductivity is strongly enhanced when one of the bands lies just
below (or touches) the Fermi level, that is, when the band is incipient. The
strong enhancement of superconductivity is because large weight of the spin
fluctuations lies in an appropriate energy range, whereas the low energy,
pair-breaking spin fluctuations are suppressed. The optimized eigenvalue of the
linearized Eliashberg equation, a measure for the strength of
superconductivity, is not strongly affected by the bare width of the incipient
band, but the parameter regime where superconductivity is optimized is wide
when the incipient band is narrow, and in this sense, the coexistence of narrow
and wide bands is favorable for superconductivity.
