I wonder if Catholics and Orthodox could eventually agree on the Divine Liturgy and mass so that one could attend either?
Well, the Oriental Orthodox will sometimes communicate Roman Catholics in the Middle East, and the Assyrian Church of the East will always communicate Roman Catholics, and conversely all of the above and the Eastern Orthodox are allowed to receive in Roman Catholic parishes. However I think its unlikely that the Eastern Orthodox will allow Roman Catholics to receive the Eucharist in EO parishes without converting until certain theological issues are concerned, and the among the Oriental Orthodox, its mainly the Syriac Orthodox who have allowed it, primarily in Turkey where there is a severe shortage of parishes, as an act of oikonomia.*
However, it is the case that the Antiochians and Syriac Orthodox are allowed to receive the Eucharist in each others parishes in the Middle East (in North America the AOCNA is an autonomous church, formerly part of the Russian Orthodox Church, that after the Soviet union and the fragmentation of the Russian church in North America into ROCOR, the OCA and the Patriarchal parishes, went under the omophorion (aegis, you might say) of the Patriarch of Antioch, but are a self-ruled church; typically, autonomous Orthodox churches like the Church of Sinai, the Church of Japan, and so on, are influenced by the parent autocephalous church only in that the latter must approve the selection of primate) and indeed, the relationship of those two churches is so close that in the Middle East at least, as opposed to in AOCNA jurisdiction in North America, they will not receive converts from each other, so if a Syriac Orthodox marries an Antiochian Orthodox, they remain members of their respective churches and can receive the Eucharist in either. A similar agreement exists between the Coptic Orthodox and the Alexandrian Greek Catholics.
The tiny Church of Sinai, which consists of St. Catharine’s Monastery and a handful of tiny chapels where the liturgy is occasionally celebrated, and whose Archbishop is the Hegumen of St. Catharine’s (that being the monastery from which a Belgian adventurer stole the Codex SInaiticus, but recently a portion was returned, and that also has the 6th century icon of Christ Pantocrator, and the very ancient icon of the Ladder of Divine Ascent based on the book by St. John Climacus, which are important icons to us as well as to Roman Catholics), has communicated Copts, and does receive with hospitality Roman Catholic pilgrims who have come to see the bush that was burned but not harmed as a theophany before St. Moses the Prophet, the aforementioned icons, and the fragment of Codex Sinaiticus (which along with Codex Vaticanus comprise the two complete manuscripts of the Alexandrian Text Type, also known as the Minority Text; the Codex Alexandrinus is partially of the Alexandrian text type, but the Gospels follow the Byzantine Text Type).
Likewise Roman Catholic churches such as the church in Bari where the relics of St. Nicholas of Myra were taken do provide Orthodox pilgrims with the myrhh that streams from his relics, which is greatly appreciated. Additionally, relations at the Church of the Holy Sepulchre and other shared holy sites in the Holy Land such as the Church of the Nativity have improved in recent years.
So it might well be the case that as we draw closer together, that the Eastern Orthodox will reciprocate the Eucharistic hospitality of the Roman Catholics. This is certainly something to pray for.
* In the case of the Armenian Catholics, the Armenian Orthodox will likely communicate any Armenian or receive them by communion, particularly after what just happened in Ngorno-Karabakh, and also most Armenian Catholics were killed in the genocide of 1915, along with an extremely large number of Armenian Apostolic; it is distressing to read in the 1911 Catholic Encyclopedia that at the time, the Armenian Catholic Church was the largest
sui juris Eastern Catholic Church and is now one of the smaller such churches.