  When two monolayers of graphene are stacked with a small relative twist
angle, the resulting band structure exhibits a remarkably flat pair of bands at
a sequence of 'magic angles' where correlation effects can induce a host of
exotic phases. Here, we study a class of related models of $n$-layered graphene
with alternating relative twist angle $\pm \theta$ which exhibit magic angle
flat bands coexisting with several Dirac dispersing bands at the Moir\'e K
point. Remarkably, we find that the Hamiltonian for the multilayer system can
be mapped exactly to a set of decoupled bilayers at {\it different} angles,
revealing a remarkable hierarchy mathematically relating all these magic angles
to the TBG case. For the trilayer case ($n = 3$), we show that the sequence of
magic angle is obtained by multiplying the bilayer magic angles by $\sqrt{2}$,
whereas the quadrilayer case ($n = 4$) has two sequences of magic angles
obtained by multiplying the bilayer magic angles by the golden ratio $\varphi =
(\sqrt{5} + 1)/2 \approx 1.62$ and its inverse. We also show that for larger
$n$, we can tune the angle to obtain several narrow (almost flat) bands
simultaneously and that for $n \rightarrow \infty$, there is a continuum of
magic angles for $\theta \lesssim 2^o$. Furthermore, we show that tuning
several perfectly flat bands for a small number of layers is possible if the
coupling between different layers is different. The setup proposed here can be
readily achieved by repeatedly applying the "tear and stack" method without the
need of any extra tuning of the twist angle and has the advantage that the
first magic angle is always larger than the bilayer case.
