The Taming of a Shrew
The Taming of a Shrew was written close to the same time as The Taming of The Shrew. Scholars have been unable to agree on which was written first or exactly how the two plays relate; one theory is that the play was a "pirated" version of Shakespeare's play, though it differs a great deal from it. Another possibility is that it was the result of a playwright creating his own version of the story, partly based on Shakespeare's version, or even that it was an earlier play that Shakespeare used as a source.
The most important difference is in the role of Christopher Sly. In A Shrew he comments on the action of the main plot throughout the play, and says, at the play's end, that he plans to go home to tame his own wife, having learned his lesson from Petruccio.
Whether this is meant as a joke or not is hard to tell: Sly, a drunkard, has just been reproved by a tapster and has been shown to be a very boorish fellow