For active-sterile mixing to be responsible for the full relic abundance of dark matter additional new physics is needed beyond the keV-scale sterile neutrino itself. The extra ingredient we consider here is the presence of self-interactions among the sterile neutrinos. We examine whether active-to-sterile conversion is amplified enough in this scenario that the observed abundance of dark matter can be obtained with a subconstraint mixing angle. This turns out never to be the case in the region we explore: either self-interactions have too small an impact and cannot escape bounds on the mass and mixing angle, or they have too great an impact and cause dark matter to be overproduced. The sharp transition from marginal to excessive effectiveness occurs because a resonance criterion is met in the effective in-medium mixing angle. Once the system goes resonant the game is as good as over, as nonlinearity in the Boltzmann equation leads to runaway production of sterile neutrinos, beginning at a plasma temperature of a few hundred MeV and typically ending at a few tens of MeV. The scenario is therefore ruled out largely by its own dynamics. In this study we focus exclusively on mediators heavier than $\sim 1$ GeV; future work will extend the analysis to lighter mediators, allowing for contact to be made with the kinds of scenarios motivated by issues of small-scale structure.

10 pages, 6 figures