If a person has an overactive thyroid, can it be only partially destroyed by a small dose of i131?

Usually not: Attempts have been made in the past to give multiple small doses of i131 until thyroid levels are normal. Unfortunately, this usually doesn't work. By the time you give enough i131 to get rid of the overactive thyroid, most people will become hypothyroid anyhow. I think the best way is to take a dose that will work, and not worry if you become hypothyroid, as this is easily treated.