Sure, dynamical ingredients like the jets carrying huge amount of luminous matter out of active galactic nuclei or the outflow from star forming activities and supernovae, for instance, have been raised as possible explanations for the apparently shallow increase in density of dark matter in galaxy cores (the "cuspiness" problem). Roughly, dynamical process in cores can -- simply by gravitational interaction -- throw dark matter back out towards the halo along with the luminous matter.

One can also step up a scale level and consider that the distribution of peculiar velocities in galaxy clusters is consistent with plenty of dark matter inside galaxy clusters but outside galaxy halos. This DM is bound to be stirred up by the moving galaxies, even if only gravitationally, and such dynamical processes will also affect the density of gas and dust in the cores of galaxy clusters (the cores of which need not be occupied by galaxies) too.

We need to explain peculiar motion of galaxy-cluster-members, and member-galaxy-vs-whole-cluster lensing behaviour too, and astronomical surveys of galaxies and clusters continue to provide plenty of data to test various theoretical approaches. Those are what propose observable consequences of self-interaction (is there dark chemistry? do dark matter particles collide and annihilate?) or is dark matter warmer than cold dark matter (if it's a naturally warm gas, then it would have a hard time gathering in the cores of galaxies and clusters, much like a warm gas has trouble gathering on the floor of a laboratory compared to a very cold gas). Or does it couple non-gravitationally but very weakly to baryons or electrons, such that it undergoes a phase change as one goes from the very dense cores of galaxies and gas-rich clusters towards the sparser edges? If one proposes atmosphere-like dynamical processes at these scales, what are the observables one expects from astronomic spectroscopy?

Spirals are certainly interesting, but there are also elliptical galaxies where the outermost hydrogen gas is in arbitrary orbit in clouds of various sizes; unlike edge-on spirals, they don't show a advancing-side/receding-side red/blueshift dipole, and where the rotating elements are large enough to measure significant dipoles, they do not strongly correlate with oblateness. More intriguingly, the measurable red/blue shift velocities of (groups of) stars within such galaxies are mostly radial, which is very different from what's seen in spirals, where rotation dominates. That radial speed is different from what would be seen if the luminous elements (including that that is luminous in infrared, radio, and so on, or material that produces absorption lines rather than emission ones) were all that determined these orbits. But a cold dark matter halo explains -- or at least is in concord with -- those orbital velocity anomalies.

And as galaxy surveys continue, neat things like giant low-surface-brightness galaxies (and their substructures) will be found more often. Their properties are good stress-tests of dark matter theories and alternatives, in that they should generate predictions for observations which will arrive within the next few years. They are also probes of largest-scale structure formation, as so far they are not found in or near dense galaxy clusters. If we start discovering GLSBs in dense regions, that would be a challenge to largest-scale distribution of dark matter as the driver of the cosmic web, which is the best current explanation of the distribution of galaxy clusters that are not gravitationally-bound with one another.