A monolayer graphene metamaterial comprising four graphene strips and four graphene blocks is proposed to produce triple plasmon-induced transparency (PIT) by the interaction of three bright modes and one dark mode. The response of the proposed structure is analyzed by using couple mode theory and finite-difference time-domain simulations, with the results of each method showing close agreement. A quadruple-mode on-to-off modulation based on synchronous or asynchronous switching is realized by tuning the Fermi levels in the graphene, its modulation degrees of amplitude are 77.7%, 58.9%, 75.4%, and 77.6% corresponding to 2.059 THz, 2.865 THz, 3.381 THz, and 3.878 THz, respectively. Moreover, the influence of the polarized light angle on triple-PIT is investigated in detail, demonstrating that the polarization angle affects PIT significantly. As a result, a multi-frequency polarizer is realized, its polarization extinction ratios are 4.2 dB, 7.8 dB, and 12.5 dB. Combined, the insights gained into the synchronous or asynchronous switching and the polarization sensitivity of triple-PIT provide a valuable platform and ideas to inspire the design of novel optoelectronic devices.