The phrase "almost fall" can have several synonyms, including "nearly stumble," "barely trip," or "just miss a misstep." Other synonyms may include "come close to falling," "almost lose your footing," or "almost take a spill." Depending on the context, the phrase can also be replaced with "teetering on the edge," "on the brink of a fall," or "a brush with a stumble." Overall, these synonyms all imply a close call with falling or tripping, but with some variation in emphasis and connotation.