Nonlinear wave mixing in optical microresonators new perospects for compact optical frequency combs with many promising applications. We demonstrate simultaneous generation of multiple frequency combs from a single optical microresonator and a single continuous-wave laser. Similar to space-division multiplexing, we generate several dissipative Kerr soliton states circulating solitonic pulses driven by a continuous-wave laser in different spatial (or polarization) modes of a MgF2 microresonator. Up to three distinct combs are produced simultaneously, featuring excellent mutual coherence and substantial repetition rate differences, useful for fast acquisition and efficient rejection of soliton intermodulation products. This method could enable the deployment of dual-and triple-comb-based methods to applications where they remained impractical with current technology.