The very nature of the epistles of the New Testament points to expected unity of the church. In other words, the apostolic writers formed their letters in such a way that it was clear that they desired the unity of the body. I'm not referring here to commands for unity but rather characteristics of the letters themselves. I've thought of several that I'm briefly discussing below. Please add any that come to mind.
-The epistles, if not sent to individuals such as Timothy, were sent to all the Christians in a city or region.
I Corinthians 1:2, "To the church of God that is in Corinth, to those sanctified in Christ Jesus, called to be saints together with all those who in every place call upon the name of our Lord Jesus Christ, both their Lord and ours." (emphasis mine)
II Corinthians 1:1, "Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother, to the church of God that is at Corinth, with all the saints who are in the whole of Achaia."
Galatians 1:2, "Paul, an apostle — not from men nor through man, but through Jesus Christ and God the Father, who raised him from the dead — and all the brothers who are with me, to the churches of Galatia."
-The epistles were not sent to particular groups within a city. All the Christians in the city or region were thought of as the church.
I Peter 1:1, "Peter, an apostle of Jesus Christ, to those who are elect exiles of the dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia."
-The epistles were designed to be shared between churches in various locations.
Colossians 4:16, "And when this letter has been read among you, have it also read in the church of the Laodiceans; and see that you also read the letter from Laodicea."
-The epistles were written to everyone in the church, not just the elders/overseers and deacons.
Philippians 1:1, "Paul and Timothy, servants of Christ Jesus, to all the saints in Christ Jesus who are at Philippi, with the overseers and deacons."
-The writers considered all the Christians to be saints. The priesthood of all believers is emphasized. No one had special status.
I Peter 2:9, "But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light."
-The epistles focus on the importance of the one anothers. All are expected to minister and serve. The commands associated with the one anothers are in the plural.
I Peter 1:22, "Having purified your souls by your obedience to the truth for a sincere brotherly love, love one another earnestly from a pure heart."
-The epistles were written to both men and women.
Colossians 1:2, "To the saints and faithful brothers in Christ at Colossae: Grace to you and peace from God our Father." (The word for "brothers" in Greek often referred to Christian brothers and sisters).
-The epistles were written for all ages to hear.
Ephesians 6:1-4, "Children, obey your parents in the Lord, for this is right. 'Honor your father and mother' (this is the first commandment with a promise), 'that it may go well with you and that you may live long in the land.' Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord."
We see that even the form of the NT letters was designed to convey the expectation of unity within the entire church. We can and should learn much from this example.