A plasmonic structure composed of a metal–insulator–metal waveguide, a stub cavity, a T-shaped cavity (T-SC), and a split-rectangular cavity (S-RC) is proposed and investigated using the finite element method. The results demonstrate triple Fano resonances in the transmission spectrum due to the interaction between cavities. The maximum sensitivity and figure of merit were 1600 nm RIU−1 and 14 455, respectively. The Fano resonance can be independently modulated by changing the structural parameters of the T-SC or S-RC, and a new Fano resonance can be generated by breaking the symmetry of the structure. Through the addition of three semi-ring cavities and a semi-disk cavity to the original structure, we obtained eight ultra-sharp and asymmetric Fano resonances, which improved the integration and performance of the structure. Therefore, the proposed device has potential applications in refractive index sensors, optical communication areas, and multi-control Fano switches.