The production cross section of neutron-rich isotopes of Ca, Zn, Te, Xe, and Pt are predicted in the diffusive multinucleon transfer reactions with stable and radioactive beams. With these isotopes one can treat the neutron shell evolution beyond $N=28$, 50, 82, and 126. Because of the small cross sections, the production of nuclei near the neutron drip line requires the optimal choice of reaction partners and bombarding energies.