A large enhancement in the production of neutron-rich projectile residues is observed in the reactions of a 25 MeV/nucleon 86 Kr beam with the neutron rich 124 Sn and 64 Ni 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 112 Sn target. The data demonstrate the significant effect 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 accounts for part of the observed large cross sections. The DIT simulation indicates that the production of neutron-rich nuclides in these reactions is associated with peripheral nucleon exchange in which the neutron skins of the neutron-rich 124 Sn and 64 Ni target nuclei may play an important role. 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.PACS numbers: 25.70.Hi,25.70.Lm Exploration of the nuclear landscape towards the neutron-drip line [1] is currently of great interest in order to elucidate the evolution of nuclear structure with increasing neutron-to-proton ratio (N/Z) [2,3] and understand important nucleosynthesis pathways [4], most notably the r-process [5]. Reactions induced by neutronrich nuclei provide invaluable information on the isospin dependence of the nuclear equation of state [6,7]. Extremely neutron-rich nuclei offer the unprecedented opportunity to extrapolate our knowledge to the properties of bulk isospin-rich matter, such as neutron stars [8,9]. The efficient production of very neutron-rich nuclides is a key issue in current and future rare isotope beam facilities around the world [10,11,12] and, in parallel, the search for new synthetic approaches is of exceptional importance.Neutron-rich nuclides have traditionally been produced in spallation reactions, fission, and projectile fragmentation [13]. In high-energy fragmentation reactions, the production of the most neutron-rich isotopes is based on a "clean-cut" removal of protons from the projectile. The world's data on fragmentation cross sections are well represented by the empirical parametrization EPAX [14]. EPAX is currently the common basis for predictions to plan rare beam experiments and facilities. In addition to the widely used projectile fragmentation approach, neutron-rich nuclides can be produced in multinucleon transfer reactions [15] and deep-inelastic reactions near the Coulomb barrier (e.g. [16,17,18]). In such reactions, the target N/Z significantly affects the production cross sections, but the low velocities of the fragments and the ensuing wide angular and ionic charge state distributions render practical applications rather limited. The Fermi energy regime (20-40 MeV/nucleon) [19] offers the unique opportunity to combine the advantages of both low-and high-energy reactions. At this energy, the synergy...