Abstract Multiple interactions of quarks and gluons in high-energy heavy-ion collisions may give rise to interesting phenomena of color charges propagating in high-density QCD matter. We study the dynamics of multi-parton systems produced in nucleus-nucleus collisions at energies corresponding to the CERN SPS and the future BNL RHIC experiments. Due to the complexity of the multi-particle dynamics we choose to employ the parton cascade model in order to simulate the development of multiple parton scatterings and associated stimulated emission processes. Our results indicate a non-linear increase with nuclear mass A of, e.g., parton multiplicity, energy density, strangeness. If multiple interactions are suppressed and only primary-primary parton scatterings (no re-interactions) are considered, we witness a linear behavior for the above quantities. It remains to be studied whether these results on the parton level, can be experimentally seen in final-state observables, such as the charged particle multiplicity, the magnitude of produced transverse energy, or the number of produced strange hadrons.