The possibility of studying particle-like states near the Fermi surfaces of exotic nuclei by using measurements of heavy-ion-induced single-nucleon pickup reactions with in-flight separated rare-isotope beams is discussed. The analysis of an exploratory data set for the intermediate-energy Be-9(Ne-20,Na-21)X proton pickup reaction measured using a Ne-20 beam at 63 MeV per nucleon is reported. The data are compared with expectations based on model calculations of the transfer reaction cross sections and the Na-21 residue spectroscopy prediction by the sd-shell model. The measured cross sections are broadly consistent with these expectations.