Quick Questions: Could have / Might have / May have

Which modal verb form(s) can complete the reply?

Mark: - Who sent these flowers?
Julie: - I'm not sure. It ..................... your mother.

• could have been
• might have been
• may have been

All three are possible!

To say that it is possible that something happened or was true in the past, we can use may/might have + past participle.

• Polly's very late. ~ She may have missed her train. (= It is possible that she missed the train)
• What was that noise? ~ It might have been a cat.

However, although might have and may have are used interchangeably, a number of people find may have incorrect if we know that something was possible, but actually did not happen.
~ You were stupid to try climbing up there. You might have killed yourself.
~ The draw against Italy might have been a turning point, but it didn't turn out like that.

May/might have ... can sometimes refer to the present or future.
~ I'll try phoning him, but he may have gone out by now.
~ By the end of this year I might have saved some money.

For more information concerning could have & might have follow this link.