  Pions of a dark sector gauge group can be strongly interacting massive
particle (SIMP) dark matter, produced by the freeze-out of $3 \to 2$
interactions, with naturally large self-interactions. We study if adding a dark
photon to the set-up can do it all: i) maintain thermalization with the visible
sector, ii) resonantly enhance the $3\to2$ interactions, thus allowing for a
perturbative pion description, and iii) provide a velocity dependent
self-interaction that can affect small scale structure formation. For $N_f=3$
this minimal setup is marginally excluded, as the required kinetic mixing is
too small to maintain thermal equilibrium with the SM. Adding an extra dark
quark opens up parameter space, and -- perhaps somewhat surprisingly -- we find
that all bounds can be satisfied for dark pion masses $m_\pi \sim
250-600\,$MeV. Dropping the small scale structure requirement iii), a viable
setup is reproduced for dark charges of $\alpha_d = 0.01-1$ and a dark pion
mass $m_\pi \geq 30$ MeV. Late time annihilations are non-negligible making the
SIMP dark pion a bit WIMPy.
