Deane Galbraith has several posts at Remnant of Giants on Luke’s use of Matthew’s Gospel and Q. Michael Bird labels this as the Holtzmann-Gundry hypothesis with reference to some of the literature (see his earlier extensive blog post on this position and Philip J. Long’s review of this section of The Gospel of the Lord: How the Early Church Wrote the Story of Jesus). In addition to some of the scholars Bird lists, I would add Maurice Casey’s view (An Aramaic Approach to Q) that Luke knew Matthew’s Gospel and had access to alternative Greek and Aramaic sources and Dennis MacDonald’s view (Two Shipwrecked Gospels) that Luke drew on Matthew’s Gospel, an enlarged Q source, and Papias’s Exposition of the Logia about the Lord.
As I shift back and forth between the Two Source and Farrer theories, this is a position I find increasingly attractive. However, for it to succeed, it must scrutinize every bit of the “double tradition” shared by Matthew and Luke and formulate persuasive criteria for what goes back to Matthew, what to a written source or sources, and what to oral tradition. This will be more complex than either the Two Source theory that Matthew and Luke were totally independent, thus all of the double tradition must go back to a shared source that many Q scholars insist was a single, coherent one with a distinctive ideology, or some versions of the Farrer theory (e.g. Michael Goulder) that Luke was always reworking the texts from Matthew’s Gospel. I think this could be an exciting research project!