I just found out about this new book:
Alan Kam-Yau Chan. Melchizedek Passages in the Bible: A Case Study for Inner-Biblical and Inter-Biblical Interpretation. De Gruyter.
"Adopting discourse analysis and text-linguistic approaches, Chan attempts to tackle the Melchizedek texts in Genesis 14, Psalm 110, and Hebrews 5-7. This study illustrates how the Melchizedek is understood and interpreted by later biblical writers. Using the blessing motif as a framework, Chan also argues that Numbers 22-24, 2 Samuel 7 and the Psalter: Books I-V (especially Psalms 1-2) provide a reading paradigm of interpreting Psalm 110."