To be clear, I'm talking about teams carrying 3 goalies on their roster.
Not a team dressing 3 goalies. I don't think there's any reasonable (or fair) scenario where a team be allowed to dress 3 goalies.
Sorry to intervene... but why would they need special provisions to carry three goalies.
All they need is the cap space and a roster spot. A third string goalie is only a league minimum salary. There's no reason teams can't squeeze a third goalie onto the roster now if they wanted.
They opt not too because they are used so infrequently, and are literally replacement level players, so prefer to keep those roster spots for forwards and defensemen who will likely see more game time and have a bigger impact.