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The only thing that would cause the icemaker to keep making ice after it's already full is a bad bin thermistor. If you open the door and look at the right side wall inside the ice compartment bucket, there is a white plastic rod sensor mounted to the right side wall. That is your bin thermistor and you'll need to replace it. If you have a full model number I can look up the part and send you a link to the sensor if you'd like so you can order it.
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