  Layers of two-dimensional materials arranged at a twist angle with respect to
each other lead to enlarged unit cells with potentially strongly altered band
structures, offering a new arena for novel and engineered many-body ground
states. For the exploration of these, renormalization group methods are an
appropriate, flexible tool that take into account the mutual influence of
competing tendencies. Here we show that, within reasonable, non-trivial
approximations, the functional renormalization group known from simpler
two-dimensional systems can be employed for the large-unit cell moir\'e
superlattices with more than 10.000 bands, remedying the need to employ ad hoc
restrictions to effective low-energy theories of a few bands and/or effective
continuum theories. This provides a description on the atomic scale, allowing
one to absorb available ab-initio information on the model parameters and
therefore lending the analysis a more concrete quantitative character. For the
case of twisted bilayer graphene models, we explore the leading ordering
tendencies depending on the band filling and the range of interactions. The
results indicate a delicate balance between distinct magnetically ordered
ground states, as well as the occurrence of a charge modulation within the
moir\'e unit cell for sufficiently non-local repulsive interaction.
