  We introduce trilayer and multilayer moir\'e heterostructures that cannot be
viewed from the ``moir\'e-of-moir\'e" perspective of helically-twisted trilayer
graphene. These ``intrinsically trilayer" moir\'e systems feature periodic
modulation of a local quasicrystalline structure. They open the door to
realizing moir\'e heterostructures with vastly more material constituents
because they do not constrain the lattice constants of the layers. In this
manuscript, we define intrinsically multilayer patterns, provide a recipe for
their construction, derive their local configuration space, and connect the
visual patterns to physical observables in material systems.
