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We propose a class of graphene-based moir\'e systems hosting flat bands onkagome and honeycomb moir\'e superlattices. These systems are formed bystacking a graphene layer on a 2D substrate with lattice constant approximately$\sqrt{3}$ times that of graphene. When the moir\'e potentials are induced by a2D irreducible corepresentation in the substrate, the model shows a rich phasediagram of low energy bands including eigenvalue fragile phases as well askagome and honeycomb flat bands. Spin-orbit coupling in the substrate can liftsymmetry protected degeneracies and create spin Chern bands, and we observespin Chern numbers up to three. We additionally propose a moir\'e system formedby stacking two graphene-like layers with similar lattice constants and Fermienergies but with Dirac Fermi velocities of opposite sign. This system exhibitsmultiple kagome and honeycomb flat bands simultaneously. Both models we proposeresemble the hypermagic model of [Scheer $\textit{et al.}$, Phys. Rev. B$\textbf{106}$, 115418 (2022)] and may provide ideal platforms for therealization of strongly correlated topological phases.

Kagome and honeycomb flat bands in moir\'e graphene