That may not have been Mike's brother you met - I think his cousin is staying with him at the moment.

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，与过去分词 been 构成完成时态，表示动作已经发生或状态已经存在。 may have been 这个结构表示对过去发生的事情的可能性推测，意思是"可能是.../也许曾经是..."。