Oedipus Rex sort of fits this bill, although it comes from a world where people didn't have the same fine-detail genre categories or expectations that we do (any more than a concept of 'twists', really). So it is a tragedy all the way through, but the first half is about a king trying to discover what is afflicting his city, and the second half about him reacting to the discovery that it is him.

Shakespeare's Julius Caesar also kills off its title character half-way through, and then, having dealt with why people might want to kil him, moves on to exploring the consequences.