Spatial division multiplexing utilizes the directionality of the light's propagating k-vector to separate it into distinct spatial directions. Here, we show that the anisotropy of orthogonal spatial solitons propagating in a single graphene monolayer results in phase-based multiplexing. We use the self-confinement properties of spatial solitons to increase the usable density of states (DOS) of this switching system. Furthermore, we show that crossing two orthogonal solitons exhibits a low (0.035 dB) mutual disturbance from another enabling independent k-vector switching. The efficient utilization of the DOS and multiplexing in real space enables data processing parallelism with applications in optical networking and computing.