Theoretical and experimental studies have verified the existence of “magic angles” in twisted bilayer graphene, where the rotation angle between layers gives rise to flat bands and consequently exotic correlated phases. Recently, magic-angle phenomena have been predicted and reported in other graphene systems, for instance, multilayers with alternating twist angles and trilayers with identical twist angles between consecutive layers. In this paper, we present a comprehensive theoretical study on flat bands in general twisted graphene systems. Using the continuum model in the chiral limit, we demonstrate the existence of flat bands in a variety of multilayers where the ratios between twist angles are rational and develop a framework for predicting magic-angle sets in trilayer configurations with arbitrary ratio of rotation angles. Our results are corroborated by tight-binding calculations. Remarkably, the technique we developed can be extended to systems with many layers of graphene. Our results suggest that flat bands can exist in graphene multilayers with angle disorder, that is, narrow samples of turbostatic graphite, point to the existence of a continuous, connected magic surface in trilayer configuration space, and compare favourably with contemporary experiments on trilayer moiré quasicrystals. Published by the American Physical Society 2024