We investigate electronic transport in doped semiconductors by using a coupled ensemble Monte Carlo molecular-dynamics (EMC-MD) scheme. An accurate, many-body description of dynamically screened impurity scattering results and is used for probing transport effects in a regime dominated by long-range Coulomb interactions. Our results clearly show that multi-ion modifications to ionized-impurity scattering play a significant role, and that simple single-site models are inadequate for realistic simulations. We find, for example, excellent agreement with experimental mobility data only with the EMC-MD technique. Furthermore, multi-ion contributions reduce the velocity autocorrelations, a trend that increases with impurity doping. Finally, in compensated materials we observe an enhanced role of collective multi-ion scattering because of decreases in free-carrier screening. The effect translates into a significant reduction of electronic mobilities.