  We show that Floquet engineering with circularly polarized light (CPL) can
selectively split the valley degeneracy of a twisted multilayer graphene (TMG),
and thus generate a controlled valley-polarized Floquet Chern flat band with
tunable large Chern number. It offers a feasible optical way to manipulate the
valley degree of freedom in moir\'{e} flat bands, and hence opens new
opportunities to study the valleytronics of mori\'{e} flat band systems. We
thus expect that many of the valley-related properties of TMG, e.g. orbital
ferromagnetism, can be switched by CPL with proper doping. We reveal a Chern
number hierarchy rule for the Floquet flat bands in a generic (M+N)-layer TMG.
We also illustrate that the CPL effects on TMG strongly rely on the stacking
chirality, which is an unique feature of TMG. All these phenomena could be
tested in the twisted double bilayer graphene systems, which is the simplest
example of TMG and has already been realized in experiment.
