It is shown that an electron, positron and ion plasma can be self-organized to a double Beltrami state – the superposition of two force-free states. The scale parameters which determine the nature of the self-organized structures are found to depend on the number densities of the plasma species. The loss of equilibrium in slowly evolving double Beltrmi states is investigated. The effects of density ratios, helicities, positron flows and energy on equilibrium are investigated. It is found that the double Beltrami state transforms to a single Beltrami state at the termination of equilibrium. It is also shown that much of the magnetic energy converts to the flow kinetic energy through catastrophic transformation.