It could -- that's the self-interacting dark matter idea -- but not at a level that is important in large galactic halos. In fact, I've seen recent suggestions that in the context of self-interacting dark matter, observations favor a velocity-dependent interaction strength that scales as v^(-4), i.e. decreases very strongly with velocity. This would make interactions irrelevant in clusters and large galaxies (which have very high velocity dispersions) and most relevant toward the centers of the smallest galaxies.