Francis A. Sullivan S.J., in his Christology of Theodore of Mopsuestia finds the theological distinctions between Antioch (prior to John of Antioch’s reconciliation with Cyril in 433) and Alexandria arising from how Theodore of Mopsuestia on the one hand and Athanasius on the other, responded to the essential Arian Syllogism: The word is the subject even of the human operations and sufferings of Christ (major premise); but whatever is predicated of the word, must be predicated of him kata phὐsin (minor premise); ergo, the nature of the Word is limited and affected by the human operations and sufferings of Christ.
The Antiochians denied the major premise (the Word is the subject of even the human operations and suffering), the Alexandrians the minor (all things predicated of the Word are done so according to nature). For the Alexandrines, and here chiefly Athanasius, the minor premise lacked the specificity which the Incarnation demanded, namely that Christ had two natures. By making this distinction, the major premise could be vigorously maintained. But it was another assumption that led the Antiochians, chiefly Theodore and Diodore of Tarsus, to accept the minor premise: that natures have subjects corresponding to the properties of its respective natures. Thus, the human nature has a human subject (namely the human person of Christ, which is distinct from the divine person of the Word). This Antiochene response can be found in later writers, particularly during the Reformation controversies over the Eucharist between the Lutherans and the Reformed. The Lutherans divinized Christ’s humanity in an almost Eutychian manner, while the Reformed, so bent on keeping the human nature of the Word away from the Eucharistic elements, refused to allow that the human nature of Christ was the result of the actions of the Word. They (I am thinking mainly of Peter Martry Vermigli, but others come to mind, including archbishop Cranmer, Heinrich Bullinger, and John Jewel) sought to deny any divine predicates to the human nature, and Martyr in particular saw the communicatio idiomatum as merely a verbal (read nominal) reality: this from a man, ironically, who was absolute in his adherence to Aristotle.
In this regard, the Lutheran and Catholic charge against the Reformed of Nestorianism, the creating of two Christ’s (a human Jesus and a divine Christ as I have heard from some Evos), becomes an all too true reality. Jewel actually refused to admit that the human nature of Christ, more importantly the enhypostasized nature, could possess certain divine attributes, particularly eternality or immensity. Though he never used this term, and I doubt he would have given someone any more than a quizzical look were it cast at him, the essential thrust of Jewel’s argument is clear: though capable of performing supernatural acts, the flesh of Christ possessed no divine properties.