Conventional single-mode coupling-of-mode (COM) theory fails to describe multimode coupling between acoustic modes in surface acoustic wave (SAW) resonators. Although multimode COM theory has been reported, explicit analytical formulas for perturbed wavenumbers and rule discovery of mutual coupling effects are still insufficient. In this work, a multimode COM model considering complete coupling terms is established for periodic grating structures. The analytical expressions of perturbed wavenumbers for two-mode coupling are derived, which directly quantifies how mutual-coupling coefficients influence dispersion relations and eigen-modes near Bragg condition. Numerical investigations reveal that both coupling strength and frequency separation between modes jointly distort Bragg stop-band features. Further, finite-length IDT admittance simulations demonstrate that even weak coupling can induce observable deviations on both main-mode resonance and remote spurious responses, indicating that resonator response cannot be simply superposed by independent single-mode results. Finally, the proposed multimode COM model is applied to fit finite-element simulation results of LN/SiO₂/SiC heterostructured SAW resonator. Compared with conventional single-mode COM, this model successfully reproduces spurious resonances far away from main resonance. This work provides an efficient theoretical tool for broadband modeling and spurious-mode analysis of multimode thin-film SAW resonators.