may: used in various polite expressions with I
might: used to politely say something about someone or something
一:
May I suggest that you consider the matter further before taking any action.
Might I just say how lovely it is to see everyone here today.
二:
May I suggest that you think carefully before rushing into this? ( can/may I suggest (=used to politely suggest a different idea )
May I ask why you took that decision?
May I suggest a better idea?
Might I ask how old you are?
[问] 老师们一中的例句为什么使用句号。
[相关资料] (不同词义的回答,葛传椝英语惯用法词典:May I make a suggestion?里的 May I...?有“你允许我……么?”的意思,是请求对方同意的一种客气语式。Might I...?比May I...?更客气些。这两句在语法上是疑问句,所以末尾用问号,但因为实际上等于请求句,所以也可以用句号。)