[en] We propose a novel mechanism to generate sterile neutrinos ν${}_s$ in the early Universe, by converting ordinary neutrinos ν${}_{\mathrm{\alpha <!--\; ??\; -->}}$ in scattering processes ν${}_s$ν${}_{\mathrm{\alpha <!--\; ??\; -->}}$→ν${}_s$ν${}_s$. After initial production by oscillations, this leads to an exponential growth in the ν${}_s$ abundance. We show that such a production regime naturally occurs for self-interacting ν${}_s$, and that this opens up significant new parameter space where ν${}_s$ 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.