In Linux, can you assign more than one group owner per directory or a file?
Say, you want to give privileged access to more than one group, or different access to different group.

Thanks in advance.

Only one group can be the direct owner of a directory, file, device, etc. However, the members of a group can be other groups. For example, on one of my boxes I have CD burners on /dev/hdc and /dev/hdd. The group owning them is cdrom. The members of cdrom are the group disk and 3 of my users.

Your permissions are fixed across the groups though. The rw permissions I have assigned to cdrom carry through to all members and can't be changed for a subset. Since there are three permission groups (user/owner, group, other/world) you may be able to achieve what you need with the 'user' or 'other' permissions.

There are also such things as ACLs if you really need them, although the code is not usually installed by default. You can really fine tune with it, but conversely, it's fiddly.