Microcombs have enabled a host of cutting-edge applications from metrology to communications that have garnered significant attention in the last decade. Nevertheless, due to the thermal instability of the microresonator, additional control devices like auxiliary lasers are indispensable for single-soliton generation in some scenarios. Specifically, the increased system complexity would be too overwhelming for dual-microcomb generation. Here, we put forward a novel approach to mitigate the thermal instability and generate the dual-microcomb using a compact system. This process is akin to mode-division multiplexing, as the dual-microcombs are generated by pumping the dual-mode of a single Si3N4 microresonator with a continuous-wave laser. Both numerical simulations and experimental measurements indicate that this innovative technique could offer a straightforward way to enlarge the soliton existence range, allowing entry into the multistability regime and triggering another microcomb alongside the main soliton pulse. This outcome not only shines new light on the interaction mechanism of microresonator modes but also provides an avenue for the development of dual-microcomb-based ranging and low phase noise microwave generation.