In the past few years, analog computing has experienced rapid development but mostly for a single function. Motivated by parallel space-time computing and miniaturization, we show that reconfigurable graphene-based multilayerss offer a promising path towards spatiotemporal computing with integrated functionalities by properly engineering both spatial- and temporal-frequency responses. This paper employs a tunable graphene-based multilayers to enable analog signal and image processing in both space and time by tuning the external bias. In the first part of the paper, we propose a switchable analog computing paradigm in which the proposed multilayers can switch among defined performances by selecting a proper external voltage for graphene monolayers. Spatial isotropic differentiation and edge detection in the spatial channel and first-order temporal differentiation and multilayers-based phaser with linear group-delay response in the temporal channel are demonstrated. In the second section of the paper, simultaneous and parallel spatiotemporal analog computing is demonstrated. The proposed multilayers processor has almost no static power consumption due to its floating-gate configuration. The spatial- and temporal-frequency transfer functions (TFs) are engineered using a transmission line (TL) model, and the obtained results are validated with full-wave simulations. Our proposal will enable real-time parallel spatiotemporal analog signal and image processing.