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This paper proposed a plasmonic resonator system, consisting of a metal-insulator-metal structure and two stubs, and a Fano resonance arose in its transmittance, which resulted from the coupling between the two stubs. On the basis of the proposed structure, a circle and a ring cavity are separately added above the stubs to create different coupled plasmonic structures, providing triple and quadruple Fano resonances, respectively. Additionally, by adjusting the geometric parameters of the system, multiple Fano Resonances obtained can be tuned. The proposed structure can be served as a high efficient refractive index sensor, yielding a sensitivity of 2000 nm/RIU and figure of merit (FOM) of <inline-formula> <math display="inline"> <semantics> <mrow> <mn>4.05</mn> <mo>&#215;</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>4</mn> </msup> </mrow> </semantics> </math> </inline-formula> and performing better than most of the similar structures. It is believed that the proposed structure may support substantial applications for on-chip sensors, slow light and nonlinear devices in highly integrated photonic circuits.