Papa John's puts soybean oil in the crust and sunflower oil in the pizza sauce, so every pizza has two seed oils in it before toppings, and the shredded cheese on all of them carries modified food starch, cellulose and sodium citrate. Their Original Crust and pizza sauce are otherwise unusually short lists.
Papa John's publishes ingredient statements for its pizza components across three pages of its own site - crusts, cheeses and sauces, then meats, then veggies - 30 components in all. Seed oils are unavoidable here: Original and Thin crusts both list soybean oil, the Gluten-Free crust uses a canola and olive blend, and the Original pizza sauce lists sunflower oil, so every pizza carries two of them before a topping goes on. 18 of the 30 components carry an additive, and the shredded cheese that goes on every pizza is one of them - modified food starch, cellulose and sodium citrate. Credit where it is due: Original Crust is six ingredients and the sauce is tomatoes, oils, sugar, salt, garlic and spices. Note this list is pizza only - wings, Papadias, the garlic dipping cup and desserts are not published.