Hybrid microresonators have served an intriguing platform for fundamental research and applied photonics. Here, we study the plasmonics-engineered coupling between degenerate optical whispering gallery modes, which can be tuned in a complex space featuring the dissipative strong, dispersive strong, and weak coupling regimes. Experimentally, the engineering of a single plasmonic resonance to a cavity mode family is examined in a waveguide-integrated high-Q microdisk, from which the complex coupling coefficients are extracted and agree well with theoretical predictions. The coupling strength over 10GHz is achieved for both dissipative and dispersive interactions, showing a remarkable enhancement compared to that induced by a dielectric scatterer. Furthermore, the far fields of hybridized cavity modes are measured, revealing the coherent interference between the radiative channels. Our results shed light on the engineering of whispering gallery modes through plasmonic resonances, and provide fundamental guidance to practical microcavity devices.