  We show that a superlattice potential can be employed to engineer topology in
massive Dirac fermions in systems such as bilayer graphene, moir\'e
graphene-boron nitride, and transition-metal dichalcogenide (TMD) monolayers
and bilayers. We use symmetry analysis to analyze band inversions to determine
the Chern number $\mathscr C$ for the valence band as a function of tunable
potential parameters for a class of $C_4$ and $C_3$ symmetric potentials. We
present a novel method to engineer Chern number $\mathscr{C}=2$ for the valence
band and show that the applied potential at minimum must have a scalar together
with a non-scalar periodic part. We discover that certain forms of the
superlattice potential, which may be difficult to realize in naturally
occurring moir\'e patterns, allow for the possibility of non-trivial
topological transitions. These forms may be achievable using an external
superlattice potential that can be created using contemporary experimental
techniques. Our work paves the way to realize the quantum Spin Hall effect
(QSHE), quantum anomalous Hall effect (QAHE), and even exotic non-Abelian
anyons in the fractional quantum Hall effect (FQHE).
