The
Atlanta Shakespeare Company is pursuing the Canon Completion Project, to become one of the few companies to have performed the entire 39-play canon (some have performed the 37-play canon, not including the later resolved disputed works). Two other companies have done this: the Royal Shakespeare Company and the King's Men (that would be Shakespeare himself).
I've only missed a few:
King John
Henry VIII
Troilus and Cressida
Timon of Athens
Antony and Cleopatra
Titus Andronicus
The Two Noble Kinsmen
Edward III (Shakespeare's newest play, admitted to the canon in the 1990s)
It is true that parts of the disputed works were contributed by other people, including some fragments by Thomas More, but Shakespeare didn't build a career on originality anyway. I've been reading some of the sources of his plays, like the Tragedy of Juliet and Romeus, and he lifted couplets intact (and sometimes more) from previous plays that likely themselves borrowed from existing sources. Disputed authorship is a gray matter before the last few centuries. no doubt Shakespeare and More both would be fascinated and perhaps a bit confused by the modern attention to originality and attribution, and even Gutenberg might be surprised at the legal nature of copyright.