We present a mechanism for producing a cosmologically significant relic density of one or more sterile neutrinos. This scheme invokes two steps: First, a population of "heavy" sterile neutrinos is created by scattering-induced decoherence of active neutrinos. Second, this population is transferred, via sterile neutrino self-interaction-mediated scatterings and decays, to one or more lighter mass (∼10 keV to ∼1 GeV) sterile neutrinos that are far more weakly (or not at all) mixed with active species and could constitute dark matter. Dark matter produced this way can evade current electromagnetic and structure-based bounds, but may nevertheless be probed by future observations.