The rheology of suspensions of non-Brownian soft spheres is studied across jamming but also across the viscous and inertial regimes using a custom pressure- and volume-imposed rheometer. The study shows that the granular rheology found for suspensions of hard spheres can be extended to a soft granular rheology (SGranR) by renormalizing the critical volume fraction and friction coefficient to pressure-dependent values and using the addition of the viscous and inertial stress scales. This SGranR encompasses rheological behaviors on both sides of the jamming transition, resulting in an approximate collapse of the rheological data into two branches when scaled with the distance to jamming, as observed for soft colloids. This research suggests that suspensions of soft particles across flow regimes can be described by a unified SGranR framework around the jamming transition.