Nuclear reactions with intermediate-energy beams in which three, four, and five nucleons are removed are expected to proceed through a combination of nondissipative and statistical processes. In an experiment at the National Superconducting Cyclotron Laboratory, in-beam gamma-ray spectroscopy was utilized to study few-nucleon removal reactions from incoming beams of 24Mg, 25Al, and 26Si projectiles to the same reaction product, 21Mg. New gamma-ray transitions and gamma -gamma coincidences in 21Mg were established using the CsI(Na) array CAESAR and the inclusive cross section for three-neutron removal from 24Mg was measured. Significant differences in the relative population of states in 21Mg from 25Al compared to 26Si were observed and found to be correlated with the spins of the 21Mg states. As a result, this intermediate regime between direct and statistical nucleon removal may have potential as a tool to deliver unique patterns of level populations in fast-beam experiments and alter isomer to ground state ratios in the production of exotic beams.