There's a great article in the New York Times today about Double Falsehood, a play allegedly based on Shakespeare's lost Cardenio. It is perhaps impossible to authenticate the play as Shakespeare's (even in part), and even so it's not regarded as a particularly good play.
I don't have this play on the Shakespeare in a Year schedule, although I do plan to include Edward III, whose claim to Shakespeare authorship is also shaky. What do you think? Should we squeeze in Double Falsehood somewhere?