Experimental studies of the simultaneous acceleration of three-charge-state ^{129}Xe^{49+,50+,51+} beam from 17 to 180 MeV/nucleon in a superconducting linear accelerator are presented. The beam parameters for each individual- and multiple-charge-state beam were measured and compared with the particle tracking simulations. Detailed measurements were performed to characterize the multiple-charge-state beam's recombination after a second-order achromat and isopath 180° bending system. As a result of the recombination of three charge states in the six-dimensional phase space, the xenon beam intensity was increased by 2.5-fold compared to the single-charge-state beam. The results presented in the Letter fully validate the possibility to produce and utilize high-quality multiple-charge-state heavy-ion beams in a large-scale superconducting linac to increase the available beam power on an isotope production target.