  Strongly interacting massive particles $\pi$ have been advocated as prominent
dark matter candidates when they regulate their relic abundance through
odd-numbered $3 \pi \to2\pi$ annihilation. We show that successful freeze-out
may also be achieved through even-numbered interactions $X X \to \pi \pi $ once
bound states $X$ among the particles of the low-energy spectrum exist. In
addition, $X$-formation hosts the potential of also catalyzing odd-numbered $3
\pi \to2\pi$ annihilation processes, turning them into effective two-body
processes $\pi X \to \pi\pi$. Bound states are often a natural consequence of
strongly interacting theories. We calculate the dark matter freeze-out and
comment on the cosmic viability and possible extensions. Candidate theories can
encompass confining sectors without a mass gap, glueball dark matter, or
$\phi^3$ and $\phi^4$ theories with strong Yukawa or self-interactions.
