The triple plasmon-induced transparency (PIT) effect based on a metal–insulator–metal waveguide structure comprising two groups of big and small disk resonators (BSDRs) is investigated theoretically and numerically. As a tool employed to explain the PIT, N-order coupled mode theory (CMT), is established, and the calculated results of the triple-PIT effect exhibit excellent consistency with finite-difference time-domain simulations. The influence of the separation between the small disk resonators on the triple-PIT response is discussed in detail through the dynamical equation. Further research shows that the central wavelengths of the triple-PIT transmission window can be adjusted with extremely low pump intensity and ultrafast optical response when monolayer graphene covers the surface of the BSDRs. Meaningfully, light traveling at resonant wavelengths can be effectively slowed down, with the highest group index reaching 368. Based on the PIT effect, a low-power and ultrafast switch is realized with a modulation amplitude of more than 93% at the corresponding wavelengths of the eight depressions. Thus, not only do the insights put forward new ideas, to the best of our knowledge, for highly tunable optoelectronic devices, but the results from the N-order CMT also offer new theory progress and references in the plasmonic waveguide structures.