Cable-driven continuum robots exhibit excellent capabilities in the unstructured environment due to their inherent compliance and dexterity. To improve the reliability and load capacity of continuum robots, increasing the number of cables is often used in the control of continuum robots. However, the number of actuators will increase with the cables. To tackle this challenge, this work proposes a method for increasing the number of cables without increasing actuators in a continuum robot through parallel platforms. The parallel platforms are used to control all the cables in the continuum robot and can be separated from the continuum robot to enable the remote drive of a manipulation arm by using the cable-tube structure. The manipulation arm is composed of several independent bending modules in series, which can be configured freely according to the demand of degrees-of-freedom. Further, each bending module is controlled independently by a parallel platform, which can avoid the mutual interference between the cables of one bending module and another one, improve the position accuracy and simplify the control difficulty of the manipulation arm. To evaluate the proposed method, this work develops a prototype of six-cable-driven continuum robot controlled by 3RPS parallel platforms and presents some basic kinematic models to describe its function, and then an experimental work characterizing its performance. Experimental results illustrated the importance of increasing the number of cables, the rationality of kinematic models of the continuum robot, and the feasibility of controlling multiple cables by a parallel platform.