We studied the production of neutron-rich nuclides in multinucleon transfer collisions of stable and radioactive beams in the mass range A∼40-60. We first presented our experimental cross section data of projectile fragments from the reaction of 40 Ar(15 MeV/nucleon) with 64 Ni, 58 Ni and 27 Al. We then compared them with calculations based on either the deep-inelastic transfer (DIT) model or the constrained molecular dynamics (CoMD) model, followed by the statistical multifragmentation model (SMM). An overall good agreement of the calculations with the experimental data is obtained. We continued with calculations of the reaction of 40 Ar (15 MeV/nucleon) with 238 U target and then with reactions of 48 Ca (15 MeV/nucleon) with 64 Ni and 238 U targets. In these reactions, neutron-rich rare isotopes with large cross sections are produced. These nuclides, in turn, can be assumed to form radioactive beams and interact with a subsequent target (preferably 238 U), leading to the production of extremely neutron-rich and even new isotopes (e.g. 60 Ca) in this mass range. We conclude that multinucleon transfer reactions with stable or radioactive beams at the energy of around 15 MeV/nucleon offer an effective route to access extremely neutron-rich rare isotopes for nuclear structure or reaction studies.