Assuming the Farrer Theory -- Matthew used Mark, and Luke used both Mark and Matthew -- is it wrong to think of each successive evangelist attempting to supplant and supersede their predecessor(s)/source(s)? Mark wrote the first-ever gospel containing the euanggelion of Jesus the Messiah with Matthew later coming along and "improving" upon the foundation that was laid by this work. Matthew retains much of Mark's narrative and creatively expanded sections of it with teaching/sayings material, a birth narrative as well as clarifying parts of Mark which expect the reader to figure things out for themselves. Luke, then, comes along and decides that he is going to craft a narrative which will present the "correct order" of things; thus recasting the accounts of Matthew and Mark in an attempt to replace them with his conception of the gospel and interpretation of the life of Jesus. A good analogy one of my professors gave while discussing this idea with him is that of a new edition of a textbook. Each new edition is an attempt to clarify, improve and ultimately replace the previous one. Could Mark, then, be understood crudely as The Gospel, 1st Edition; Matthew as the 2nd Edition and Luke as the 3rd Edition of the Gospel genre?
The jury is still out for me whether or not John was familiar with any or all of the synoptics. But should he have been familiar with any of them, could the same intention be present in the Fourth Gospel (however, unlike the synoptics, John doesn't carry over much of his source material, so the analogy might not be appropriate in this context). But more on that topic in the weeks to come.
An interesting counter-point was raised while discussing this idea with a classmate of mine. He noted that we seem to have the conception of a four-gospel canon in the late 2nd c. which seems to militate against the idea of a secondary and tertiary gospel replacing their predecessor(s)/source(s). Although this is true, this need not reflect the actual intentions of the evangelists themselves. Perhaps Matthew's purpose was to improve upon, and ultimately replace, Mark's gospel account for his community/church. The same could go for Luke. Whether or not they succeeded, we will never know. But should this have been the case, my bet is that they were indeed successful within their own communities. However, in the end, their accounts spread beyond their respective communities and began circulating amongst other groups of Christians who most likely would have been unaware of any of these intentions by the authors. Therefore, you do not see whole sail disappearance of any of the four canonical gospels -- although Mark seems to have been copied less than the other two in antiquity.
Of course, these are just some nascent musings. But ones which I intend to follow up on in due course.