I have worked in mental hospitals, and have had issues with people becoming "water intoxicated" due to their psychosis. So despite what people tell you , you absolutely can drink too much water. Is it likely for a person not insane? No. But yeah....it can happen.

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It doesn't hurt your kidneys, but can give you heart attack and other similar. You can make it worse by drinking distilled water, as it will leach more minerals from your body.