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[en] We propose a novel mechanism to generate sterile neutrinos ν in the early Universe, by converting ordinary neutrinos ν in scattering processes νν→νν. After initial production by oscillations, this leads to an exponential growth in the ν abundance. We show that such a production regime naturally occurs for self-interacting ν, and that this opens up significant new parameter space where ν make up all of the observed dark matter. Our results provide strong motivation to further push the sensitivity of X-ray line searches, and to improve on constraints from structure formation.