Using multipoint measurements from the Cluster ion spectrometry instruments and the research with adaptive particle imaging detectors, we identified new properties of multiple energy-dispersed ion structures in the plasma sheet boundary layer (PSBL). On 14 February 2001 at about 4.5 R_E midnight local time, the PSBL was highly structured, showing several large-scale dispersed ion structures, which were substructured into several (up to four) beamlets with a quasiperiodicity of 1-3 min in the spacecraft frames. The different spacecraft (SC) recorded the first dispersed ion structures at different times and on different L shells at the outer edge of the PSBL within 2 min. Three different energy dispersions were associated with the dispersed ion structures. (1) The energy dispersion of the larger-scale structures was due to the decreasing energy of individual beamlets, covering energies from 2 to >40 keV. (2) Individual beamlets of each large-scale structure showed themselves energy dispersion along the peak flux line with varying slopes, but in all cases these slopes were steeper compared to the dispersion associated with the large-scale structure. (3) A third steep energy dispersion occurred at the beginning of each beamlet and covered an energy range from a few keV to > 100 keV. This dispersion was associated with recurrent impulsive acceleration processes at 11-27 R_E radial distance with a quasiperiodicity of 1-3 min. Moreover, most beamlets showed pitch angle dispersion. Superimposed on the dispersed ion structures were two transient ion injections, which had the same energy dispersion slope as described in item 3 (above), suggesting an association with the beamlets. The beamlets and one of the transient ion injections were recorded for different ion species: hydrogen, helium, and oxygen. Furthermore, echoes of beamlets were recorded, which makes this the first observation of bouncing ions in the PSBL. The echoes showed higher energy fluxes than the initial beamlets, indicating additional acceleration during subsequent current sheet crossings. Gradual thermalization of the initial beamlets after multiple current sheet crossings possibly led to the formation of the central plasma sheet. SC 1 and SC 3, longitudinally separated by only 100 km, recorded very different beamlet structures, which we interpret as a spatial effect; the two beamlet structures mapped into different magnetotail regions and underwent different spatiotemporal histories. Two possible scenarios are discussed to understand the spatiotemporal history of this highly structured PSBL.