The agents belong to different AGs, the customer needing is to automatically login the agents to ALL the AGs with no chances to select/unselect the singular AG. The automatic login has been set in the Agent privileges but they could un-thick some AGroups anyway, that's way I supposed that belonging just to one VAG the problem would be solved.
It's a fact that practically the Agents would work like a singular Agent Group but depending on the Supervisor the Agents have to be included in one or more AGS time by time.