We propose a novel mechanism to generate sterile neutrinos
$\nu_s$ in the early Universe, by converting ordinary neutrinos
$\nu_a$ in scattering processes $\nu_s\nu_a\to\nu_s\nu_s$.
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.