The development of twisted bilayer TMDs established a new field for the investigation of correlated electron phases in 2D materials on triangular lattices. Compared to TBG, twisted bilayer TMDs allow the access to quantitative different layer orientations with respect to the twisting angle. This results in the case of AB stacking to a suppressed interlayer tunneling from the bottom to the top layer valence band. Recent studies connected this to an SU(4) symmetry, which perturbations can break down to SU(2)xSU(2). Continuing this idea, we enhance this ansatz to twisted multilayer systems concluding in a theoretical SU(N)xSU(M) symmetry. The idea is also motivated by recent realisations of SU(2)xSU(6) systems in cold atomic gases. To analyse the correlated phases of the resulting Hubbard models, we generalise the functional renormalization group approach for correlated fermion systems to efficiently incorporate the high symmetries.