Can and could refer to capability, though could often implies some doubt.
- Unlike our previous server, this one can support up to 50 users.
- I suppose our old car could make the drive to California.
May and might refer to permission or possibility.
- When time permits, you may start working on the project.
- If everything goes as planned, you may finish the project early.
- We might be able to go to the party after the game.