The multicontinuous network nature of polymer nanostructures provides them with many opportunities to fabricate multifunctional materials with specific mechanical, transport, optical, and other novel properties. In this paper, we generate an effective design principle to craft a series of multicontinuous network structures with controllable channels, including multicontinuous gyroid and O-70 network morphologies via the self-assembly of ABC-type block copolymers. Importantly, we achieve a much wider (similar to 25%) compositional range than that of AB diblock copolymers (similar to 3%), which would increase the widespread application of these multicontinuous polymer networks. Even for the simplest ABC linear system, this method is valid for generating multicontinuous network structures, where gyroids and O-70 are found to possess large phase regions. This finding can theoretically explain the experimental observation of gyroid and O-70 phases. We believe that our proposed design principle along with the calculated phase diagram provides a compelling panacea for the fabrication of multicontinuous 3D network nanostructures.