"Build fire under" can be replaced by several different synonyms depending on the context of its usage. Some of the most common synonyms for this phrase include "motivate," "encourage," "prompt," "stimulate," and "spur." These synonyms can be used in various situations where there is a need to motivate or push someone towards achieving a specific goal. For example, a boss might want to build fire under their employee to complete a task within a specific timeframe. Similarly, a coach might try to build fire under their athletes to push them to perform their best during a competition. The synonyms for "build fire under" all convey a sense of urgency and determination, motivating individuals to take actions that lead them towards success.