This work proposed a multiple mode Fano resonance-based refractive index sensor with high sensitivity that is a rarely investigated structure. The designed device consists of a metal–insulator–metal (MIM) waveguide with two rectangular stubs side-coupled with an elliptical resonator embedded with an air path in the resonator and several metal defects set in the bus waveguide. We systematically studied three types of sensor structures employing the finite element method. Results show that the surface plasmon mode’s splitting is affected by the geometry of the sensor. We found that the transmittance dips and peaks can dramatically change by adding the dual air stubs, and the light–matter interaction can effectively enhance by embedding an air path in the resonator and the metal defects in the bus waveguide. The double air stubs and an air path contribute to the cavity plasmon resonance, and the metal defects facilitate the gap plasmon resonance in the proposed plasmonic sensor, resulting in remarkable characteristics compared with those of plasmonic sensors. The high sensitivity of 2600 nm/RIU and 1200 nm/RIU can simultaneously achieve in mode 1 and mode 2 of the proposed type 3 structure, which considerably raises the sensitivity by 216.67% for mode 1 and 133.33% for mode 2 compared to its regular counterpart, i.e., type 2 structure. The designed sensing structure can detect the material’s refractive index in a wide range of gas, liquids, and biomaterials (e.g., hemoglobin concentration).