  The recent experimental realization of spin-orbit (SO) coupling for ultracold
bosons and fermions opens an exciting avenue for engineering quantum matter
that may be challenging to realize in solid state materials such as SO coupled
spin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been
experimentally realized, the generation of two-dimensional (2D) SO coupling and
its topological properties are largely unexplored. Here we propose an
experimental scheme for realizing a 2D Dresselhaus-type SO coupling in a square
lattice for spin-1 Fermi gases. Because of the extended spin degree of freedom,
many interesting topological phases could exist without relying on lattice
point group symmetries that are crucial in solid state materials. These exotic
phases include triply-degenerate points, quadratic band touching, a large Chern
number ($C=5$) superfluid with 5 Majorana modes, triple-Weyl fermions, etc. Our
scheme can be generalized to larger spins and provides a new route for
engineering topological quantum matter by utilizing large spin degrees of
freedom, instead of specific lattice symmetries.
