Polite expression of uncertainty, attached after a plain-form clause, adjective, or noun phrase. It is the polite counterpart of かもしれない and is common in careful conversation and writing.
See also: かもしれない
It may rain tomorrow.
The train may be delayed.
He may have already gone home.
でしょう expresses a confident guess closer to 'probably', while かもしれません emphasizes mere possibility, closer to 'maybe/might'.
A polite fixed expression corresponding to かもしれない, historically analyzable as か + も + 知れません, literally suggesting that something 'cannot be known' for sure. In modern use it functions as a modal expression meaning 'may' or 'might' and is usually written in kana.