About ten years ago Maguire and Smith identified parts of All's Well that are collaborations with Middleton, but this is still disputed. Middleton added musical sequences to Macbeth. Henry VI part 1 was likely collaborative with Nashe and others. It's not so much that Shakespeare wrote the important parts and had others fit the less important bits in; it's more like one can tell which bits he wrote because they are so much better than, say, Fletcher or Kyd.

Taming of THE Shrew and Merchant of Venice were not collaborative, according to my missus, who is a Shakespeare scholar, although Taming of A Shrew (in the quarto) may have had collaboration. So I'd be interested to read the arguments presented. My missus also says that a good example of a collaborative work is Sir Thomas More, the currently accepted position is that WS wrote about three pages, although my wife's more interested in the history of the plays in performance, rather than who wrote what bits. But it interests me as my MSc thesis was on stylometric identification of authorship of seventeenth century political papers.

Shakespeare valued his poetry more, and he worked on their publication, which he didn't for the plays. He was a theatre man, a player as well as a playwright, so he was collaborative almost by nature.

But as for those who claim that Shakespeare didn't write his plays (particularly supporters of de Vere), they generally boil down to them being so posh, or servile, that they cannot stomach the idea that a Midlands grammar school boy could write what he did.