  The observation of strongly-correlated states in moir\'e systems has renewed
the conceptual interest in magnetic systems with higher SU(4) spin symmetry,
e.g. to describe Mott insulators where the local moments are coupled
spin-valley degrees of freedom. Here, we discuss a numerical renormalization
group scheme to explore the formation of spin-valley ordered and unconventional
spin-valley liquid states at zero temperature based on a pseudo-fermion
representation. Our generalization of the conventional pseudo-fermion
functional renormalization group approach for $\mathfrak{su}$(2) spins is
capable of treating diagonal and off-diagonal couplings of generic spin-valley
exchange Hamiltonians in the self-conjugate representation of the
$\mathfrak{su}$(4) algebra. To achieve proper numerical efficiency, we derive a
number of symmetry constraints on the flow equations that significantly limit
the number of ordinary differential equations to be solved. As an example
system, we investigate a diagonal SU(2)$_{\textrm{spin}}$ $\otimes$
U(1)$_{\textrm{valley}}$ model on the triangular lattice which exhibits a rich
phase diagram of spin and valley ordered phases.
