A terahertz metasurface consisting of a graphene ribbon and three graphene strips, which can generate a significant triple plasmon-induced transparency (triple-PIT), is proposed to realize a multifunction switch and optical storage. Numerical simulation triple-PIT which is the result of destructive interference between three bright modes and a dark mode can be fitted by coupled mode theory (CMT). The penta-frequency asynchronous and quatary-frequency synchronous switches can be achieved by modulating the graphene Fermi levels. And the switch performance including modulation depth (83.5% < MD < 93.5%) and insertion loss (0.10 dB < IL < 0.26 dB) is great excellent. In addition, the group index of the triple-PIT can be as high as 935, meaning an excellent optical storage is achieved. Thus, the work provides a new method for designing terahertz multi-function switches and optical storages.