  Second-order topological semimetals (SOTSMs) are featured with hinge Fermi
arcs. How to generate them in different systems has attracted much attention.
We propose a scheme to create exotic SOTSMs by periodic driving. Novel Dirac
SOTSMs, with a widely tunable number of nodes and hinge Fermi arcs, the
adjacent nodes having the same chirality, and the coexisting nodal points and
loops, are generated at ease by the periodic driving. When the time-reversal
symmetry is broken, our scheme permits us to realize hybrid-order Weyl
semimetals with the coexisting hinge and surface Fermi arcs. Our Weyl
semimetals possess a rich hybrid of 2D sliced zero- and $\pi/T$-mode
topological phases, which may be any combination of the normal insulator, Chern
insulator, and second-order topological insulator. Enriching the family of
topological semimetals, our scheme supplies a convenient way to artificially
synthesize exotic topological phases by periodic driving.
