This paper proposes new types of models that have coaxial magnetic gear (CMG) configurations to increase torque transmission capability. They have flux concentrating structures at the outer low speed rotor, and permanent magnets (PMs) are embedded in the space between stationary pole pieces. The torque performances of the proposed models are compared with those of a basic CMG model. The harmonic torque components due to air gap field harmonics are also analyzed to investigate the torque contribution of each harmonic by using finite element analysis (FEA) and the Maxwell stress tensor. The proposed CMG model is optimized to have high torque density with low torque ripples by response surface methodology (RSM). Compared to the basic CMG model, the proposed model has a huge increase in transmitted torque density, and is very advantageous in term of PM use.