  Semi-annihilation is a generic feature of dark matter theories with
symmetries larger than Z_2. We explore a model based on a Z_4-symmetric dark
sector comprised of a scalar singlet and a "wino"-like fermion SU(2)_L triplet.
This is the minimal example of semi-annihilation with a gauge-charged fermion.
We study the interplay of the Sommerfeld effect in both annihilation and
semi-annihilation channels. The modifications to the relic density allow
otherwise-forbidden regions of parameter space and can substantially weaken
indirect detection constraints. We perform a parameter scan and find that the
entire region where the model comprises all the observed dark matter is
accessible to current and planned direct and indirect searches.
