We designed and investigated a plasmonic nanosensor with ultra-high sensitivity and tunability, which is composed of a metal–insulator–metal (MIM) waveguide integrated with a side-coupled resonator (SR) and metal baffle. Its high performance is derived from Fano resonance, which is generated by the interaction between the modes of the SR and the baffle, and it can be precisely tuned by adjusting the parameters of the SR. Further investigation based on the incorporation of a side-coupled rectangular-ring resonator (SRR) generates three distinct Fano resonances, and the Fano resonance can be accurately tuned by manipulating the parameters of the resonators within the system. Our proposed plasmonic system can serve as a highly sensitive refractive index nanosensor, achieving a sensitivity up to 1150 nm/RIU. The plasmonic structures featuring independently tunable triple Fano resonances open new avenues for applications in nanosensing, bandstop filtering, and slow-light devices.