Lake Michigan drains a little into the Mississippi now. Engineers reversed the flow of the Chicago River & it became the Chicago ship & sanitary canal. You can guess the sanitary part.
Yes, I know about the Chicago River and ship and "sanitary" canal. The engineers didn't have to tunnel or dig very deep, so I'm amazed nature didn't do that. There is just a small rise of ground along the Great Lakes that keeps them flowing east instead of south. If there had been even one significant breach at any time since the lakes were formed, the lakes would have dug their own canal to the Mississippi, or more likely, to the Ohio River.