Edgar Allan Poe's story "William Wilson" is one work you may want to consider; "Pudd'nhead Wilson," by Mark Twain, is another. Any literary work that deals with twins might be worth exploring. Apparent twins appear in Dickens's A Tale of Two Cities.
Twins in Contemporary Literature and Culture, by Julia De Nooy, has been described by its publisher as follows:
Stories of twins are told with astonishing frequency in contemporary culture. Films and novels from recent decades repeatedly tell of the stranglehold of brotherly love, the evil twin who steals her sister's lover, the homicidal mutant twin, the reunion of twins separated at birth, warring twins, and confusion between look-alikes. Juliana de Nooy asks why we keep telling twin tales and how these have been transformed in recent retellings to reflect the preoccupations of the times.
A book titled Twins in Children's and Adolescent Literature, by Dee Storey, has been described by its publisher as follows:
From the first publication of The Bobsey Twins in 1904 to titles published in 1992, Storey annotates over 300 books that feature twins. Readers will be able to locate popular stories as well as some of the finest children's and adolescent literature in the country, and they will be able to track characters through a number of information sources. The author summarizes each book, describes the family life of the twins in it and the characters' feelings about being twins, and lists topics pertinent to the story. An unusual feature of the bibliography is the inclusion of comments made by authors who have shared their reasons for writing about twins. An index shows whether the twins are main, secondary, or minor characters.
Shakespeare's Twelfth Night and The Comedy of Errors would also be worth exploring in relation to the topic of duality in literature.
I would suggest Mary Shelley's Frankenstein. The story has been suggested to hold evidence of both Victor and his monster as being representative of Shelley herself. Also, Victor and the monster could be seen as mirrors.
The Master of Ballantrae is also a novel about twinning and duality. It is, of course, far less famous or read than Dr Jekyll and Mr Hyde but it is worth mentioning. It's also all about coming to grips and eventually coming to terms with your unconscious, with death in life and evil impulses or what brings the worst instead of the best in you...!
I have read Twelfth Night and now that you mention it, that makes sense. How ever I havent read any of those other ones so I will have to look into them when I have time.