  We point out that current constraints on dark matter imply only that the
majority of dark matter is cold and collisionless. A subdominant fraction of
dark matter could have much stronger interactions. In particular, it could
interact in a manner that dissipates energy, thereby cooling into a
rotationally-supported disk, much as baryons do. We call this proposed new dark
matter component Double-Disk Dark Matter (DDDM). We argue that DDDM could
constitute a fraction of all matter roughly as large as the fraction in
baryons, and that it could be detected through its gravitational effects on the
motion of stars in galaxies, for example. Furthermore, if DDDM can annihilate
to gamma rays, it would give rise to an indirect detection signal distributed
across the sky that differs dramatically from that predicted for ordinary dark
matter. DDDM and more general partially interacting dark matter scenarios
provide a large unexplored space of testable new physics ideas.
