There is no option to have several Layers assigned to one Object. However, you can change the Layer via Takes. In this way, you can set up different Groups, as one would have with the “Set-Theory”.
Another way might be to have a hierarchy with Layers
https://help.maxon.net/us/#11074
A less attractive way would be, to follow a specific naming convention, and since this can be filtered, it can be bookmarked. Perhaps those bookmarks are then used in an additional Object manager.
Besides that, since I have no further information why you needed that, something that comes to mind is the Selection Object, which can hold a group of objects when reactivated, all similar parameters can be edited at once, as visibility [editor/render].
If you like to have a multi-label option, this would be then a suggestion to Maxon. It could work as the labels in MacOS-X, but since each layer has an option to switch off crucial parts of the object, I see a conflict there, which you might address in the suggestion, if you have an idea, like what rules are given in case of a conflict.
https://www.maxon.net/en-us/support/suggestions/