I once worked on a team of SREs where the workload was so atrocious that we had HR make up new virtual employees Team On-call Primary and Team On-call Secondary and, other than the manager, they were the only accessible team members. We gave these virtual employees their own laptops and phones. When your shift ended, or you needed a break, you handed the gear to the next guy. We didn't have a formal schedule because it was common to get burned out in just three or four days, or if it was a rare calm period you might hang on to the laptop a bit longer until you got a chance to get properly throttled.

It worked exceptionally well because then the other employees were unable to individually bother team members. The team name in the HR directory was something vague and reported to the skip level, so unless you were in the know, we were totally invisible to the rest of the org. For some context we were keeping many millions of dollars of daily transactions afloat and it was not unusual to receive death threats from business folks when they couldn't do their jobs.

I don't miss it remotely, but I sometimes miss being a member of an invisible force with superuser privileges, with the blessing to unfuck anything we saw fit.