Yes, forces between bodies within a system can affect the acceleration of the system. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it. If two bodies within a system exert forces on each other, those forces will contribute to the overall net force acting on the system. As a result, the acceleration of the system will be affected by these forces.

For example, consider a system consisting of two objects connected by a spring. If one of the objects is pulled, it will exert a force on the spring, which in turn will exert a force on the other object. These forces will cause both objects to accelerate, resulting in a change in the overall motion of the system.

Another example is the motion of planets in the solar system. The gravitational forces between the planets and the sun contribute to the acceleration of each planet, causing them to move in their respective orbits.

Therefore, forces between bodies within a system can indeed affect the acceleration of the system. These forces can cause changes in the motion of individual objects within the system, as well as the overall behavior of the system as a whole.