  Following a general protocol of periodically driving static first-order
topological phases (supporting surface states) with suitable discrete symmetry
breaking Wilson-Dirac masses, here we construct a hierarchy of higher-order
Floquet topological phases in three dimensions. In particular, we demonstrate
realizations of both second-order and third-order Floquet topological states,
respectively supporting dynamic hinge and corner modes at zero quasienergy, by
periodically driving their static first-order parent states with one and two
discrete symmetry breaking Wilson-Dirac mass(es). While the static surface
states are characterized by codimension $d_c=1$, the resulting dynamic hinge
(corner) modes, protected by \emph{antiunitary} spectral or particle-hole
symmetries, live on the boundaries with $d_c=2$ $(3)$. We exemplify these
outcomes for three-dimensional topological insulators and Dirac semimetals,
with the latter ones following an arbitrary spin-$j$ representation.
