Even SIMP miracles are possible

Strongly interacting massive particles $\pi$ have been advocated as prominent dark matter candidates when they regulate their relic abundance through odd-numbered $3\pi \to 2\pi$ annihilation. We show that successful freeze-out may also be achieved through even-numbered interactions $XX\to \pi \pi$ 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 $3\pi \to 2\pi$ 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.