  Apparently, some form of local superconducting pairing persists to
temperatures well above the maximum observed $T_c$ in underdoped cuprates,
\textit{i.e.} $T_c$ is suppressed due to the small phase stiffness. With this
in mind, we consider the following question -- Given a system with a high
pairing scale $\Delta_0 $ but with $T_c$ reduced by phase fluctuations, can one
design a composite system in which $T_c$ approaches its mean-field value,
$T_c\to T_{MF}\approx \Delta_0/2\$? Here, we study a simple two component model
in which a "metallic layer" with $\Delta_0=0$ is coupled by single-particle
tunneling to a "pairing layer" with $\Delta_0 >0 $ but zero phase stiffness. We
show that in the limit that the bandwidth of the metal is much larger than
$\Delta_0$, $T_c$ of the composite system can reach the upper limit $T_c
\approx\Delta_0/2$.
