There are several synonyms for the phrase "fall over backwards", which means to go out of one's way to do something or to make a great effort. Some of the alternatives include "bend over backwards", "go the extra mile", "exert oneself", "strain every nerve", and "do everything one can". All of these expressions suggest a considerable amount of effort, sacrifice, or dedication to a particular cause or task. Whether you are trying to impress someone or achieve a personal goal, these synonyms offer a variety of ways to describe your commitment and determination, no matter how challenging the path may be.