Refresh supplementary group memberships without logging in again?

You can start new login from your session

$ su - your_login

It doesn't affect your running process. If you are using Xserver, you can start xterm and type this command (affect only this terminal session) The only way to make it persistient is to finish your session and start it again

I don't think so. But you can use the newgrp command to spawn a new shell with the new group. This is not permanent.

newgrp superawesomegroupname

You'll need to log your users off-then-on-again.

You can do:

exec su -l $USER

That implicitly refreshes the groups list without having to exit the terminal.