I’m really not sure what you are asking here. Each particular Church of the Byzantine Rite celebrates the
Divine Liturgy of St. John Chrysostom, using chant patterns that are unique to their own tradition (albeit with common origins).
While there are some parallels and common responses in some instances, I’m not sure how the chant for the Divine Liturgy might be adapted for the Mass in entirety.
That said, it will be interesting to see how some of this hymnody is adapted for the Pontifical Mass to be celebrated next month during the
Pope’s visit to Lebanon, but it appears that those common elements will become opportunities to use chant of the various traditions, as noted in the linked article.
While I don’t think there is such a thing as a full adaptation of Byzantine chant for the Latin Mass. I’d be happy to be proven wrong - could be interesting!