  Topological phases with a widely tunable number of edge modes have been
extensively studied as a typical class of exotic states of matter with
potentially important applications. Although several models have been shown to
support such phases, they are not easy to realize in solid-state systems due to
the complexity of various intervening factors. Inspired by the realization of
synthetic spin-orbit coupling in a cold-atom system [Z. Wu {\it et al.},
Science \textbf{354}, 83 (2016)], we propose a periodic quenching scheme to
realize large-topological-number phases with multiple edge modes in optical
lattices. Via introducing the periodic quenching to the Raman lattice, it is
found that a large number of edge modes can be induced in a controllable manner
from the static topologically trivial system. Our result provides an
experimentally accessible method to artificially synthesize and manipulate
exotic topological phases with large topological numbers and multiple edge
modes.
