By this time next year, they may have completed their round-the-world trip.

may 是情态动词，表示"可能、也许"，用来表达不确定的推测。 have 是助动词，在这里与过去分词 completed 构成现在完成时态，表示"已经完成"的动作。 may have completed 表示"可能已经完成"，用于对过去发生事情的推测。