Well technically all of the specialty restaurants have an upcharge, or a fee. But any of the dining packages will cover that so you can dine at any of them at no additional charge. That is what the package purchase price covers. (Chef's Table is excluded and would require an additional fee). Izumi is a la carte and we don't include that in the package as we never reach the fee allowance when we dine there.
And to be clear, there is the Unlimited Dining Package, which covers all specialty restaurants for dinner every night on board, and I believe also includes a couple of lunches. The other packages, such as the 3 night you refer to is for any restaurant for dinner on any three nights, with the first one typically being on day one or two. But they are separate packages - there is no such thing as a UDP 3 night package..
So if your TA provided one night and you purchase the 3 night package, you will have 4 total nights at a specialty restaurant. And you can dine multiple times at any of them within the total nights allowed with your package.