The concept and general layout of a new high-power proton multistage isochronous cyclotron is presented. Key design features include the use of large-diameter cyclotron rings having low magnetic fields and the coaxial nesting of several cyclotron stages. The proposed Coaxial-Ring Cyclotrons (CRC) accelerator system has several advantages as compared to conventional cyclotrons. It has wide turn-to-turn separation of orbits, high energy gains per turn with small number of turns in each cyclotron stage, to produce high space-charge-limited beam current, simplified beam injection and extraction at low loss, an ability to inject and simultaneously accelerate multiple independent beams, and to extract different energy beams from the intermediate orbits of cyclotron stages. One or several Radio Frequency Quadrupole (RFQ) injectors are used to provide the necessary high brightness injection. Thus, a high-current, 1.5-GeV highly-efficient and cost-effective accelerator system is conceived, specifically to serve as the proton driver in several applications of the Accelerator Driven Transmutation Technologies (ADTT), and also to serve as a photon cancer therapy source, a materials processing source, as well as to act as a high-quality accelerator for the conduct of fundamental research in physics with intense beams of neutrons, neutrinos, muons and mesons. This paper describes the general layout of the nested five stages of cyclotrons, to produce 1.0-to-1.5-GeV, 1.0-to-20-mA average-current protons in single-beam injection, or higher currents by multiple-beam injection, fitting into the 70-m diameter main ring and the inner circular hall of the existing 6-GeV Yerevan Electron Synchrotron, and converting all related facilities.