Everything in the galaxy orbits the center of the combined mass of the entire galaxy. So could the center of the combined mass of the entire galaxy change if there were no external forces acting on that galaxy ? (By external I mean forces outside of the galaxy)
I will assume you are talking about the center of mass.
If there's no external forces, the center of mass would conserve it's momentum. So, it would stay in constant speed, whatever what that speed is, with respect to whatever inertial frame of reference.
This happens because Newton's third law. In the summation of all forces, the internal forces will cancel out, leaving the external forces.