Let 'bitcoind' run by user 'bitcoin' in Linux. Chown 'bitcoin-cli' to 'bitcoin:root' and set chmod '4750' (u+s flag). Then every root-privileged user be able to run 'bitcoin-cli' even if 'bitcoind' runs by user 'bitcoin'. For example: 'bitcoin-cli getinfo' or 'sudo bitcoin-cli getinfo'
We need to patch 'util.cpp' by this pull request to get actual path for EUID instead of HOME dir, when you use 'u+s' flag.