[en] The multiple beam accelerator MBE-4 is a device for research toward a heavy ion driver for inertial confinement fusion, based on the induction linac concept. Its main goal is proof of the principle of current amplification by acceleration and controlled self-similar beam pulse compression. Into the 16-m long device four beams, each with an initial current of 10 mA are injected from a Marx-driven diode at 200 keV. The current amplification is up to nine-fold, with a final beam energy of about 800 keV in the middle of the bunch. Now that all the apparatus' accelerator sections have been completed, installed and aligned, and its unaccelerated transport properties have been studied, our experimental research has reached the crucial phase of implementing appropriate accelerator schedules that approximate self-similar current-pulse compression. These schedules are established through a close interplay of computations using a one-dimensional simulation code and a manual empirical tuning procedure. In a first approach, with a rather vigorous schedule that uses most of the accelerator modules to their voltage limits, we have determined the limits of our capability for controlled pulse compression, mainly due to waveform shaping of the driving pulse-forming networks. We shall report on these results. In the future, we will also aim for gentler schedules that would model more closely an inertial confinement fusion scenario. 8 refs., 11 figs., 1 tab