Matthean Posteriority: An Exploration of Matthews's Use of Mark and Luke as a Solution to the Synoptic Problem is a $112 book by Robert K. MacEwen (London: Bloomsbury T & T Clark, 2015) reviewed in April 2016 in the Catholic Biblical Quarterly (78/2) 373-75 by Warren Carter. It's more than an exploration and less than a endorsement.
MPH proponents included Gottlob Christian Storr, Johann Gottfried Herder, Christian Gottlob Wilke and among moderns most notably Martin Hengel.
C. 2 applies 7 tests: (1) Mammon, (2) do not store up treasure, (3) permanence of law, (4) greetings & peace in missions, (5) Beelzebub (6) care for animals on Sabbath, (4) copper, silver, gold in mission, Of these the strongest for MPH are #1, #2, #4, and #7.
Strings of verbatim words were applied to these Synoptic theories: Two-Gospel (Lk uses Mt, Mk uses both, the Griesbach Hypothesis) the Two Document (Q and Mark), the Farrer (Mt. uses Mk, Lk uses both, and there is no Q), and the MPH. He concluded all have problems, but MPH has the fewest.
Ch. 3 is a very long study of "alternating primitiveness", 'MacEwen claimed Mt more primitive persuasively only only at Mt. 7:11 "good things"" vs. Lk 11:13 "Holy Spirit".
Similarly, "The Critical Edition of Q...primitiveness of Mt's wordings is a little more frequent than in Lk, a finding that seems to support the Farrer Hypothesis more than the MPH.
For an apologia for MPH, MacEwen suggests "Matthew omits material that features morally ambiguous characters, or that is difficult to understand, or that is contradictory, or that dishonors God, and so on. The third issue concerns 'discordant parallels.' " "He accounts for these differences throught the use of differnet sources.
From pg. 375: "MacEwen concludes that while the MPH is useful, the Two Document Hyposthesis has generaly a 'slight edge over the MPH' (p.l 185)"
"MacEwens conclusion that the MPH merits further consideration seems reasonable."
In criticism of both Carter and MacEwen I would hold that the virtues of the MPH extend as far as rightly placing Matthew last in the chain, but we should find all three Synoptics are really using common sources or a common source that evolved. Why limit ourselves to extand gospels when it is so obvious there is an underlying Proto-Gospel (or more sources than one)?