We created graphene blisters that cover and seal an annular cylinder-shaped microcavity in a SiO2 substrate filled with a gas. By controlling the pressure difference between the gas inside and outside of the microcavity, we switch the graphene membrane between multiple stable equilibrium configurations. We carried out experiments starting from the situation where the pressure of the gas inside and outside of the microcavity is set equal to a prescribed charging pressure, p0 and the graphene membrane covers the cavity like an annular drum, adhered to the central post and the surrounding substrate due to van der Waals forces. We decrease the outside pressure to a value, pe which causes it to bulge into an annular blister. We systematically increase the charging pressure by repeating this procedure causing the annular blister to continue to bulge until a critical charging pressure pc(i) is reached. At this point the graphene membrane delaminates from the post in an unstable manner, resulting in a switch of graphene membrane shape from an annular to a spherical blister. Continued increase of the charging pressure results in the spherical blister growing with its height increasing, but maintaining a constant radius until a second critical charging pressure pc(o) is reached at which point the blister begins to delaminate from the periphery of the cavity in a stable manner. Here, we report a series of experiments as well as a mechanics and thermodynamic model that demonstrate how the interplay among system parameters (geometry, graphene stiffness (number of layers), pressure, and adhesion energy) results in the ability to controllably switch graphene blisters among different shapes. Arrays of these blisters can be envisioned to create pressure-switchable surface properties where the difference between patterns of annular versus spherical blisters will impact functionalities such as wettability, friction, adhesion, and surface wave characteristics.