Diet Coke
Diet Coke does not use a modified form of the Coca-Cola recipe, but instead an entirely different formula. The controversial New Coke, introduced in 1985, used a version of the Diet Coke recipe that contained high fructose corn syrup and had a slightly different balance of ingredients. In 2004, Coca-Cola introduced Coca-Cola C2, which it claims tastes much closer to Coca-Cola but contains half the carbohydrates. In 2005, the company introduced Coca-Cola Zero (replaced by "Coca-Cola Zero Sugar" in 2017), a sugar-free variation of regular Coca-Cola.
Dr Pepper
As with Coca-Cola, the formula for Dr Pepper is a trade secret, and allegedly the recipe is kept as two halves in safe deposit boxes in two separate Dallas banks. A persistent rumor since the 1930s is that the drink contains prune juice, but the official Dr Pepper FAQ refutes this with "Dr Pepper is a unique blend of natural and artificial flavors; it does not contain prune juice." The origin of the rumor is unknown; some believe it was started by a deliveryman for a competitor trying to cast aspersions based on prune juice's laxative effects, but it may simply be because many people feel that Dr Pepper tastes similar to prune juice.