Biological molecular motors are high-performance nanomachines that convert chemical energy into mechanical motion via chemomechanical coupling. Their reaction cycles typically comprise a series of intermediate chemical states between the initial and final primary states. However, the influence of these intermediate states on motor performance has not yet been fully explored. In this study, we investigate the impact of intermediate states on the motor kinetics using a reaction-diffusion model. In most cases, the intermediate states accelerate the motor by lowering the effective barrier height. This acceleration is particularly pronounced when an external load is applied to the motor, implying the practical importance of the intermediate states. The intermediate states can also slow down the reaction in some cases, such as the slow reaction limit with asymmetric kinetics. Our findings provide practical insights into the design principles behind the high performance of biological molecular motors, as well as the development of efficient artificial molecular motors.