  Dark matter semi-annihilation is a process through which two dark matter
candidates annihilate to a single dark matter particle and a non-dark matter
particle. Such processes are common when the symmetry stabilizing the dark
matter differs from $\mathbb{Z}_2$ and can lead to qualitatively different
phenomenology. In this work, we study the viability of semi-annihilation models
including one or two inert multiplets. For one multiplet, we show that there
does not exist any viable model in which semi-annihilation is efficient. For
two multiplets, semi-annihilation can be efficient, but the number of viable
and technically natural models is limited. We then perform a detailed study of
the most promising model, showing that the correct relic abundance can be
obtained for a wide range of masses.
