The phrase "add fuel" refers to the act of intensifying or exacerbating a situation. There are numerous synonyms for this phrase, such as "fan the flames," "stoke the fire," and "pour oil on the fire." All of these express the idea of making a situation worse or more intense. Other synonyms include "incite," "provoke," and "inflame," which are more direct ways of describing the act of adding fuel to a fire. Using these synonyms can help to add variety and nuance to your writing, while also making it more engaging and impactful.