The efficient production of neutron-rich nuclei has been a challenge and is a central theme at current and future rare-isotope facilities. Nuclides with high neutron excess can be reached by transferring multiple neutrons from the target to the projectile and/or by stripping protons from the projectile in multinucleon transfer reactions. Beam energies range from the Coulomb barrier to Fermi energies, about 15–35 MeV/nucleon. The authors analyze two reactions, Kr+Ni and Kr+Sn, each previously measured at 15 MeV/nucleon at the MARS recoil separator at the Texas A&M Cyclotron Institute. Systematic comparisons with calculations from two well-known models followed by a deexcitation description provide significant insight into the reaction mechanisms and indicate that multiple charge-exchange channels, along a diagonal `southeast’ path in the nuclear chart, offer an efficient route to neutron-rich nuclides.