What type of cheese is available as an extra on the menu?

American cheese is the correct choice for an extra cheese option available on the menu at Jack in the Box. This type of cheese is popular for its creamy texture and mild flavor, which complements a variety of menu items, especially burgers and sandwiches. It's a common choice among fast-food chains due to its melting properties, making it an ideal topping that enhances the overall taste and experience of the meal.

While Swiss cheese, cheddar cheese, and blue cheese are all recognized for their unique tastes and uses, they do not specifically represent the standard extra cheese option commonly found on the Jack in the Box menu. American cheese is more consistently requested by customers looking for that classic fast-food flavor profile.