We propose a novel mechanism to generate sterile neutrinos νs in theearly Universe, by converting ordinary neutrinos να in scatteringprocesses νsνα→νsνs. After initial production byoscillations, this leads to an exponential growth in the νs abundance. Weshow that such a production regime naturally occurs for self-interactingνs, and that this opens up significant new parameter space where νsmake up all of the observed dark matter. Our results provide strong motivationto further push the sensitivity of X-ray line searches, and to improve onconstraints from structure formation.<br