A 3D numerical study on surface plasmon resonance is presented for a multilayer Au/dielectric/Au nanocrescent structure adhered to a dielectric cylinder. Investigations are carried out on the structure’s coupling modes, local field enhancement (LFE) and plasmon tuning capability. The cavity coupling via the cylinder is found to be dominant in tuning the plasmon wavelength. This provides the possibility of tailoring the device's plasmon band by adjusting the cylinder’s size and material. By using a cylinder with higher permittivity, the plasmon peak significantly shifts to the near- or mid-infrared regime without increasing the size of the crescents, thus increase of radiation loss can be fully avoided. Extra crescent layers can also be added to the structure to induce intra-particle couplings among Au crescents and enlarge the areas of the hot-spots, without shifting the plasmon band. The LFE of the multiple-layer structure is shown to be dramatically increased through the intra-particle coupling among the Au crescents, compared with a single layer Au nanocrescent structure. Further increase of LFE can be achieved by substituting semiconductors for the dielectrics in the structure due to the charge transport at metal-semiconductor interfaces.