Are there refrigerators with a remote compressor?
Commercial refrigeration units are available which place the compressor in a remote location. There's a good summary of the pros and cons of such a setup at Katom Restaurant Supply which is rather comprehensive.
One thing to consider is that a typical home air conditioner is about the equivalent of a refrigerator with a remote compressor.
A post two years ago on Houzz website has about 20 comments with nothing conclusive with respect to residential systems, but the expected reference of commercial/restaurant sources.
I'd expect that you'd have to pay the premium for a commercial unit.