  We propose a class of graphene-based moir\'e systems hosting flat bands on
kagome and honeycomb moir\'e superlattices. These systems are formed by
stacking 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 a
2D irreducible corepresentation in the substrate, the model shows a rich phase
diagram of low energy bands including eigenvalue fragile phases as well as
kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift
symmetry protected degeneracies and create spin Chern bands, and we observe
spin Chern numbers up to three. We additionally propose a moir\'e system formed
by stacking two graphene-like layers with similar lattice constants and Fermi
energies but with Dirac Fermi velocities of opposite sign. This system exhibits
multiple kagome and honeycomb flat bands simultaneously. Both models we propose
resemble the hypermagic model of [Scheer $\textit{et al.}$, Phys. Rev. B
$\textbf{106}$, 115418 (2022)] and may provide ideal platforms for the
realization of strongly correlated topological phases.
