You can use either can or could to indicate possibility. Examples:
You could read the book to earn extra credit.You can use can in making a request, but you could also use could. The word could is, perhaps, more formal.)
You can read the book to earn extra credit if you want.
The word could is, of course, used to express possibility. ("It could happen.")
The word might expresses possibility. for exanmple, "A person might respond to your request" means it is a possibility but not a certainty. It could happen, but we don't know if it will.