Abstract: We consider a scenario that we call Partially Interacting Dark Matter (PIDM). This scenario contains self-interacting dark matter, but it is not the dominant Dark Matter component. Even if PIDM contains only a fraction of the net dark matter density, comparable to the baryonic fraction, the subdominant componentaEuroTMs interactions can lead to interesting and potentially observable consequences. Our primary focus will be the special case of Double-Disk Dark Matter (DDDM), in which self-interactions allow the dark matter to lose enough energy to lead to dynamics similar to those in the baryonic sector. We explore a simple model in which DDDM can cool einotfciently and form a disk within galaxies, and we evaluate some of the possible observational signatures. The most prominent signal of such a scenario could be an enhanced indirect detection signature with a distinctive spatial distribution. Such scenarios also predict additional dark radiation degrees of freedom that could soon be detectable and would ininot,uence the interpretation of future data, such as that from Planck and from the Gaia satellite.