We used angle-resolved photoemission spectroscopy and thermoelectric power to study the poorly explored, highly overdoped side of the phase diagram of Ba(Fe1−xCox)2As2 high-temperature superconductor. Our data demonstrate that several Lifshitz transitions—topological changes of the Fermi surface—occur for large x. The central hole barrel changes to ellipsoids that are centered at Z at x∼0.11 and subsequently disappear around x∼0.2; changes in thermoelectric power occur at similar x values. Tc decreases and goes to zero around x∼0.15—between the two Lifshitz transitions. Beyond x=0.2 the central pocket becomes electron-like and superconductivity does not exist. Our observations reveal the importance of the underlying Fermiology in electron-doped iron arsenides. We speculate that a likely necessary condition for superconductivity in these materials is the presence of the central hole pockets rather than nesting between central and corner pockets.