  The thermal relic density of dark matter is conventionally set by two-body
annihilations. We point out that in many simple models, $3 \to 2$ annihilations
can play an important role in determining the relic density over a broad range
of model parameters. This occurs when the two-body annihilation is
kinematically forbidden, but the $3\to 2$ process is allowed; we call this
scenario "Not-Forbidden Dark Matter". We illustrate this mechanism for a vector
portal dark matter model, showing that for a dark matter mass of $m_\chi \sim
\text{MeV - 10 GeV}$, $3 \to 2$ processes not only lead to the observed relic
density, but also imply a self-interaction cross section that can solve the
cusp/core problem. This can be accomplished while remaining consistent with
stringent CMB constraints on light dark matter, and can potentially be
discovered at future direct detection experiments.
