  We provide a novel setup for generalizing the two-dimensional pseudospin
S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general
pseudospin-S. We engineer these band structures as a nearest-neighbor hopping
Hamiltonian involving stacked triangular lattices. We obtain multi-layered low
energy excitations around half-filling described by a two-dimensional Dirac
equation of the form H=v_F S\cdot p, where S represents an arbitrary spin-S
(integer or half-integer). For integer-S, a flat band appears, whose presence
modifies qualitatively the response of the system. Among physical observables,
the density of states, the optical conductivity and the peculiarities of Klein
tunneling are investigated. We also study Chern numbers as well as the
zero-energy Landau level degeneracy. By changing the stacking pattern, the
topological properties are altered significantly, with no obvious analogue in
multilayer graphene stacks.
