Current amplification of heavy-ion beams is an integral feature of the induction linac approach to heavy-ion fusion (HIF). In this paper we report on amplification experiments conducted on a single beam of the Multiple Beam Experiment (MBE-4), a heavy-ion (Cs+) induction linac. Earlier MBE-4 experiments [H. Meuth et al., Nucl. Instrum. Methods Phys. Res. A 278, 153 (1989)] had demonstrated up-to-9× current amplification but had been accompanied by an up-to-2× increase of normalized transverse emittance. Experiments to pinpoint the causes of this emittance growth indicated various factors were responsible, including focusing aberrations and mismatch difficulties between the injector diode and the accelerator transport lattice, a localized quadrupole misalignment problem, and the interaction of transversely large beams with the nonlinear elements of the focusing lattice. Following ameliorative measures, new current amplification experiments, both with and without acceleration, showed that current amplifications of up to 3× and line charge density increases of up to ≈2× could be achieved without increasing the beam’s normalized transverse emittance. Finally, both the transverse beam dynamics, and beam current and energy measurements were accurately modeled by numerical particle-in-cell simulations and longitudinal dynamics codes, respectively.