The agent who is listing the property may know more, but you really need to check with Southampton Town Trustees Office as this home is waterfront and regulations are pretty tight these days. They will not give you a definite yeah or nay without full permit application, but they will give you an indication about whether or not it might be considered, then you can take a view. If I was a betting person, I would say it's unlikely given the layout of the house in relationship to the wetlands area, but I could be wrong. By the way, we can show you a house close to this which already has a pool right by the beach at a fraction of the price. House would need work, but a house renovation is a lot easier than getting a pool permit for a waterfront property. Good Luck!