One of the synonyms for the phrase "add fuel to fire" is "pour oil on troubled waters." Just like adding fuel to a fire makes it more intense, pouring oil on troubled waters often makes a situation worse. Similarly, "fan the flames" is another synonym that refers to adding more fuel to an already heated situation. "Stir the pot" and "provoke" are also synonyms that convey the idea of making a situation more contentious. These phrases are often used to describe situations where someone is intentionally or unintentionally making a situation more difficult to resolve, rather than helping to calm it down.