The possibility of simultaneously accelerating particles with a range of charge-to-mass ratios ( approximately 20%) to the same energy is proposed and demonstrated for a superconducting linac. Uranium ions stripped in a foil with eight charge states have been accelerated through a portion of the ATLAS linac from 286 to 690 MeV, with 94% of the injected uranium in the accelerated beam. Emittance of the resultant beam has been measured and the energy spread was 1.3% compared to 0.4% for a single charge state. This development has immediate application to the high-intensity acceleration of heavy ions that are limited by ion-source intensities, such as the proposed Rare Isotope Accelerator Facility.