Abstract The production of neutron-rich rare isotopes around the Fermi energy is investigated in the present work. A large enhancement in the production of neutron-rich projectile residues has been observed in the reactions of a 25 MeV/nucleon 86Kr beam with the neutron rich 64Ni and 124Sn targets relative to the predictions of the EPAX parametrization of high-energy fragmentation, as well as relative to the reaction with the less neutron-rich 112Sn target. The present data demonstrate the significant influence of the target neutron-to-proton ratio (N/Z) in peripheral collisions at Fermi energies. A hybrid model based on a deep-inelastic transfer code (DIT) followed by a statistical de-excitation code was found to account for part of the observed large cross sections. The DIT simulation indicates that the neutron skins of the neutron-rich 64Ni and 124Sn target nuclei play an important role in the production mechanism. From a practical viewpoint, such reactions between massive neutron-rich nuclei offer a novel synthetic avenue to access extremely neutron-rich rare isotopes towards the neutron-drip line.