The Electric Dipole Moment (EDM) is a very sensitive probe of CP-violation beyond the Standard Model, and it as been measured in many systems such as atoms, neutrons, etc. The EDM of composite systems may be sensitive to several elementary level CP-violating processes, but the theoretical evaluations of the CP-violation at different physical (atomic, nuclear, hadronic, elementary) hierarchies are required to unveil them. In this context, we are particularly interested in which CP-violating processes are enhanced in a given system, or vice versa. In this proceedings contribution, we will give an overview of the enhancement and suppression of CP-violation in processes contributing to the EDMs of composite systems.