  We propose a novel mechanism to generate sterile neutrinos $\nu_s$ in the
early Universe, by converting ordinary neutrinos $\nu_\alpha$ in scattering
processes $\nu_s\nu_\alpha\to\nu_s\nu_s$. After initial production by
oscillations, this leads to an exponential growth in the $\nu_s$ abundance. We
show that such a production regime naturally occurs for self-interacting
$\nu_s$, and that this opens up significant new parameter space where $\nu_s$
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.
