Compared with graphene, two-dimensional (2D) transition metal sulfides, represented by mono-/few-layer MoS ₂, have tunable non-zero bandgap, and thus their applications in optoelectronic devices are more advantageous. By using classical electromagnetic theory and finite element method (FEM), we investigate the cavity coupled plasmon polaritons (CCPPs) formed through the coupling between cavity modes in a resonator and plasmons in monolayer MoS ₂, particularly calculate and verify the properties of the high-order CCPPs. In previous work, it was demonstrated that the substrates, defects, and polycrystalline grains of the CVD grown monolayer MoS ₂usually induce weak electron localization, which leads to the deviation from the Drude model based on the approximation of free electron gas. Therefore, here we use the Drude-Smith model with characteristic parameters obtained experimentally to describe the optical conductivity of monolayer MoS ₂in our theoretical calculation and simulation. Then, we not only derive and solve the dispersion equations of the high-order CCPPs, but also verify the existence and analyze the properties of these high-order modes. Specifically, there are three types of CCPPs in the asymmetric cavity-monolayer MoS ₂system, i.e. the FP-like-modes (FPLMs), the surface-plasmon-like modes (SPLMs), and the quasi-localized modes (QLMs). Among them, the FPLMs and QLMs can support high-order modes whereas the SPLMs only support the fundamental modes. According to our model, we calculate the wave localization properties for the 7th-order and 8th-order FPLM, the 3rd-order and 6th-order QLM, and the SPLM. These theoretical results are in good agreement with the simulation results. Moreover, the effects of weak electron localization are also shown by comparing the field distributions of the CCPPs based on the Drude model with those based on the Drude-Smith model. It is found that weak electron localization can reduce the coupling between the cavity modes and the plasmons in monolayer MoS ₂. These results can deepen our understanding of the excitation of plasmons in 2D materials as well as the modulation of their properties. Furthermore, the theoretical model can also be extended to other plasmonic systems related to low-dimensional and topological quantum materials.