I'm pretty sure the station will be able to keep its cat, one way or another. A cat keeps mice down, even if it's not a good mouser. And it's widely accepted that petting an animal eases stress.

And who wants to tell the firefighters whom you might need to save your life that they can't keep their kitty?

Some years back, we had a fire station with a pot-bellied pig. It stayed under the radar.
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I'm pretty sure that a group of people who co-ordinate all their meals can manage to co-ordinate the care of a cat.

And if all else fails, there's midnight acquisition...