This study examines the interactions between modes in a plasmonic structure consisting of a rectangular cavity edge-coupled to a semi-ring cavity. Analysis of magnetic field distributions reveals that the low-order resonant mode in the semi-ring cavity is strongly coupled with the resonant mode in the rectangular cavity. Additionally, higher-order resonant modes exhibit significant interaction with the waveguide mode and weak coupling to the resonant modes in the rectangular resonator. Understanding these mode coupling mechanisms could offer theoretical insights for the advancement of highly integrated optical switching, sensing, and slow light devices.