This work studies the effect of a high-density correction to the Boltzmann-Uehling-Uhlenbeck (BUU) dynamics, i.e., the inclusion of triple scattering in heavy-ion reactions at intermediate incident energies. By using both schematic model calculations and the modified BUU simulations with triple scatterings incorporated, it has been suggested that the inclusion of triple scattering into the reaction dynamics could lead to an enhancement of the high-energy component in the nucleon distribution at an early stage of the reaction. An interesting point of this study is to indicate that this enhancement has been retarded considerably by the Fermi motion and mean field. Thus, as far as this effect is considered, the incorporation of triple scattering is not sufficient to account for the difference between the conventional BUU predicted and measured subthreshold particle production data, such as pions. Our results also show that these conclusions do not rely on the approximations adopted in the existing treatments of triple scatterings.