Apparently, some form of local superconducting pairing persists up to temperatures well above the maximum observed T c in underdoped cuprates; 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 ⌬ 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 → T MF Ϸ ⌬ 0 / 2? Here, we study a simple two-component model in which

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... a "metallic layer" with ⌬ 0 =0 is coupled by single-particle tunneling to a "pairing layer" with ⌬ 0 Ͼ 0 but zero phase stiffness. We show that in the limit where the bandwidth of the metal is much larger than ⌬ 0 , the T c of the composite system can reach the upper limit T c Ϸ ⌬ 0 / 2. where ͗rrЈ͘ denotes nearest neighbors. H f is the Hamiltonian of the pairing layer: PHYSICAL REVIEW B 78, 094509 ͑2008͒