In this study, a novel plasmonic refractive index sensor is proposed, featuring a metal–insulator–metal (MIM) waveguide coupled with a composite cavity structure consisting of a double-arc rectangle cavity, a bridge cavity and a three-half-ring configuration cavity. Finite element simulations are used to analyze the transmission characteristics and magnetic field distributions. The results show that six resonance peaks can be produced by three independent resonators. Moreover, there is a good linear relationship between these resonance wavelengths and the structural parameters of the resonators. Then, the refractive index sensing performances of the structure are analyzed by changing the refractive index of the medium within the resonator. The highest sensitivities of the peaks in their resonators are 1732, 2800 and 4568 nm/RIU, respectively. In addition, the proposed structure is tested for the simultaneous detection of the peanut oil concentration of three different blended oils: soybean-peanut, peanut-rapeseed and peanut-sunflower. The ability of the sensor to accurately and simultaneously measure these different oil mixtures highlights its potential for biochemical sensing.