  Motivated by measurements of compressibility and STM spectra in twisted
bilayer graphene, we analyze the pattern of symmetry breaking for itinerant
fermions near a van Hove singularity. Making use of an approximate SU(4)
symmetry of the Landau functional, we show that the structure of the
spin/isospin order parameter changes with increasing filling via a cascade of
transitions. We compute the feedback from different spin/isospin orders on
fermions and argue that each order splits the initially 4-fold degenerate van
Hove peak in a particular fashion, consistent with the STM data and
compressibility measurements, providing a unified interpretation of the cascade
of transitions in twisted bilayer graphene. Our results follow from a generic
analysis of an SU(4)-symmetric Landau functional and are valid beyond a
specific underlying fermionic model. We argue that an analogous van Hove
scenario explains the cascade of phase transitions in non-twisted Bernal
bilayer and rhombohedral trilayer graphene.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons