Neutron-rich Co isotopes from N = 34 to 40 were studied through multinucleon transfer by bombarding a U-238 target with a 460 MeV Zn-70 beam at LNL. Gamma-recoil coincidences were recorded identifying the ions by a high-acceptance magnetic spectrometer (PRISMA) and detecting the gamma radiation by an array of HPGe clover detectors (CLARA). The results are discussed in comparison with the predictions of large-scale shell-model calculations.