A periodic patterned graphene-based terahertz metamaterial comprising three transverse graphene strips and one longitudinal continuous graphene ribbon is proposed to achieve a dynamically tunable quadruple plasmon-induced transparency (PIT) effect. Further analysis of the magnetic field distribution along the x-direction shows that the quadruple-PIT window can be produced by the strong destructive interference between the bright mode and the dark mode. The spectral response characteristics of the quadruple-PIT effect are numerically and theoretically investigated, and the results obtained by the finite-difference time-domain (FDTD) simulation fit well with that by the coupled mode theory (CMT) calculation. In addition, two hepta-frequency asynchronous switches are achieved by tuning the Fermi energy of the graphene, and their maximum modulation depths are 98.9% and 99.7%, corresponding to the insertion losses of 0.173 dB and 0.334 dB, respectively. Further studies show that polarization light has a significant impact on the quadruple-PIT, resulting in a polarization-sensitive switch being realized with a maximum modulation depth of 99.7% and a minimum insertion loss of 0.048 dB. In addition, when the Fermi energy is equal to 1.2 eV, the maximum time delay and group refractive index of the quadruple-PIT can be respectively as high as 1.065 ps and 3194, and the maximum delay-bandwidth product reaches 1.098, which means that excellent optical storage is achieved. Thus, our proposed quadruple-PIT system can be used to design a terahertz multi-channel switch and optical storage.