Reload a Linux user's group assignments without logging out

Problem

When assigning a user's secondary group list using: is it possible to force this group assignment to take effect without logging out all running sessions? This would be very useful in the situation where a Screen session exists with many running shells, as the entire session essentially needs to be destroyed to make the group assignment take effect. I think I can change the user's primary group in a running shell using the command - is there some alternative that would work for secondary groups? Ideally, I'd want something that would take effect in each shell without being run manually in every one, but failing that, maybe some way of forcing Screen to execute the same command in each.