I got fed up with the weak remote range with my 1998 Deville and I decided to "fix" it. The box circled in red is the remote receiver, I know this because my car stops responding to my remote when I unplugged it. You have to remove your rear seat in order to get access(refer to my upcoming stereo guide in the audio/video section), the entire job takes about half an hour, you'll need any kind of thin wire(20~16 gauge) and a way to attach wire to a piece of conducting metal. I just used a broken clock's powercord and two small crimp connectors in my toolbox.
Once the seat is removed you can pop this little box off easily by pressing the two top plastic tabs downward. Flip it over and you'll see a small metal clip - that is the receiver's antenna. Simply crimp or solder a piece of wire to each end and you're done. The range of the improvement depends on the length of your wires and where you put them, I crimped two 20" pieces of typical lamp wires to each end and evenly ran them horizontally and around the black rack. I now can lock my car in my room, my car is more than 50 feet away and there are four walls between us.
As for exactly how far you can extend the range, technically if you run enough wires in your car or used an actual powered radio antenna you can probably boost the range to over 100 feet. Just make sure you don't press it accidentally.