The Layers of Matthew - I

There is no separate "Q Document."

The only sources we need to solve the "Synoptic Problem" are Matthew and Mark.

The substratum of the sayings portion of Matthew was in Hebrew (Matthew I).

At some point it became necessary to translate Matthew I into Greek (Matthew II).

This Mathew II, although in Greek, was still too "Jewish" for Paul's purposes, so editorial changes were made, giving us Luke I, still essentially a sayings gospel, but more acceptable to the Gentiles.

Peter's public speeches were recorded by Mark. They were probably not intended to be a separate gospel, but they provided the narrative portions of Matthew and Luke.

Along with the Markan narrative, further sayings material (e.g. the Beatitudes not included in the  Lukan list) was added to Matthew II, giving us Matthew III. The evangelist of the Gospel of Luke may never have seen this expanded Matthew.

The Markan narrative was also added to Luke I, giving us Luke II.

At this point, there was no longer a need for a separate Gospel of Mark, but it was included in the Canon because Peter was the leader of the apostles and an eyewitness.

This theory can explain everything that we observe, including the Minor Agreements.