I think it is worth noting what the web site of the American Antiochian Archdiocese says (quoting St Justin Popovich) about the nature of the Church:
'The Unity and Uniqueness of the Church
Just as the Person of Christ the God-man is one and unique, so is the Church founded by Him, in Him, and upon Him. The unity of the Church follows necessarily from the unity of the Person of the Lord Christ, the God-man. Being an organically integral and theanthropic organism unique in all the worlds, the Church, according to all the laws of Heaven and earth, is indivisible. Any division would signify her death. Immersed in the God-man, she is first and foremost a theanthropic organism, and only then a theanthropic organization. In her, everything is theanthropic: nature, faith, love, baptism, the Eucharist, all the holy mysteries and all the holy virtues, her teaching, her entire life, her immortality, her eternity, and her structure.
Yes, yes, yes; in her, everything is theanthropically integral and indivisible Christification, sanctification, deification, Trinitarianism, salvation. In her everything is fused organically and by grace into a single theanthropic body, under a single Head — the God-man, the Lord Christ. All her members, though as persons always whole and inviolate, yet united by the same grace of the Holy Spirit through the holy mysteries and the holy virtues into an organic unity, comprise one body and confess the one faith, which unites them to each other and to the Lord Christ.
The Christ-bearing apostles are divinely inspired as they announce the unity and the uniqueness of the Church, based upon the unity and uniqueness of her Founder — the God-man, the Lord Christ, and His theanthropic personality:
“For another foundation can no man lay than that is laid, which is Jesus Christ” (I Cor. 3:11)
Like the holy apostles, the holy fathers and the teachers of the Church confess the unity and uniqueness of the Orthodox Church with the divine wisdom of the cherubim and the zeal of the seraphim. Understandable, therefore, is the fiery zeal which animated the holy fathers of the Church in all cases of division and falling away and the stern attitude toward heresies and schisms. In that regard, the holy ecumenical and holy local councils are preeminently important. According to their spirit and attitude, wise in those things pertaining to Christ, the Church is not only one but also unique. Just as the Lord Christ cannot have several bodies, so He cannot have several Churches. According to her theanthropic nature, the Church is one and unique, just as Christ the God-man is one and unique.
Hence, a division, a splitting up of the Church is ontologically and essentially impossible. A division within the Church has never occurred, nor indeed can one take place, while apostasy from the Church has and will continue to occur after the manner of those voluntarily fruitless branches which, having withered, fall away from the eternally living theanthropic Vine — the Lord Christ (Jn. 15:1-6). From time to time, heretics and schismatics have cut themselves off and have fallen away from the one and indivisible Church of Christ, whereby they ceased to be members of the Church and parts of her theanthropic body. The first to fall away thus were the gnostics, then the Arians, then the Macedonians, then the Monophysites, then the Iconoclasts, then the Roman Catholics, then the Protestants, then the Uniates, and so on—all the other members of the legion of heretics and schismatics.'