The cross sections and velocity distributions of projectile-like fragments from the reaction of 25 MeV/nucleon 86 Kr + 64 Ni have been measured using the MARS recoil separator at Texas A&M, with special emphasis on the neutron rich isotopes. Proton-removal and neutron pick-up isotopes have been observed with large cross sections. A model of deep-inelastic transfer (DIT) for the primary interaction stage and the statistical evaporation code GEMINI for the deexcitation stage have been used to describe the properties of the product distributions. The results have also been compared with the EPAX parametrization of high-energy fragmentation yields. The experimental data show an enhancement in the production of neutron-rich isotopes close to the projectile, relative to the predictions of DIT/GEMINI and the expectations of EPAX. We attribute this enhancement mainly to the effect of the extended neutron distribution (neutron "skin") of the 64 Ni target in peripheral interactions of 86 Kr with 64 Ni. The large cross sections of such reactions near the Fermi energy, involving peripheral nucleon exchange, suggest that, not only the N/Z of the projectile and the target, but also the N/Z distribution at the nuclear surface may properly be exploited in the production of neutron-rich rare isotopes. This synthesis approach may offer a fruitful pathway to extremely neutron-rich nuclei, towards the neutron-drip line.