  Due to the observed superconductivity, the alternating twisted trilayer
graphene (ATTLG) has drawn great research interest very recently, in which
three monolayer graphene (MLG) are stacked in alternating twist way. If one or
several of the MLG in ATTLG are replaced by a multilayer graphene, we get a
double twisted multilayer graphene (DTMLG). In this work, we theoretically
illustrate that, if the DTMLG has a mirror symmetry along z direction like the
ATTLG, there exists a mirror symmetry decomposition (MSD), by which the DTMLG
can be exactly decoupled into two subsystems with opposite parity. The two
subsystems are either a twisted multilayer graphene (single twist) or a
multilayer graphene, depending on the stacking configuration. Such MSD can give
a clear interpretation about all the novel features of the moir\'{e} band
structures of DTMLG, e.g. the fourfold degenerate flat bands and the enlarged
magic angle. Meanwhile, in such DTMLG, the parity becomes a new degree of
freedom of the electrons, so that we can define a parity resolved Chern number
for the moir\'{e} flat bands. More importantly, the MSD implies that all the
novel correlated phases in the twisted multilayer graphene should also exist in
the corresponding DTMLGs, since they have the exact same Hamiltonian in form.
Specifically, according to the MSD, we predict that the superconductivity
should exist in the (1+3+1)-DTMLG.
