Yes you can, and possibly are - it can lead to a condition known as hyponatremia whereby your blood plasma is diluted to such an extent that it ceases to function correctly. The symptoms include headache, mental confusion and fatigue - rather like dehydration - in exterme cases it can lead to unconciousness, coma or even death. You must ensure that you are keeping up your intake of salts and sugars to ensure that your blood plasma is not diluting.
You shouldn't need to drink that much unadorned water in a day - especially if this is in addition to water in the form of food and other beverages - if you are doing so it is a possible sign of a medical problem such as kidney trouble or diabetes.
That said, I do not know your personal circumstances - climate, body mass, daily activities - if you are concerned then speak to a doctor.