Viable Palatini-$f(R)$ cosmologies with generalized dark matter

We study the formation of large-scale structure in universes dominated by dark matter and driven to accelerated expansion by $f(R)$ gravity in the Palatini formalism. If the dark matter is cold, practically all of these models are ruled out because they fail to reproduce the observed matter power spectrum. We point out that if the assumption that dark matter is perfect and pressureless at all scales is relaxed, nontrivial alternatives to a cosmological constant become viable within this class of modified gravity models.