One of the more dangerous oversights in the East/West dialogue has been in overlooking the unique contribution of Stoicism to Christianity in the West. IMHO, the tendency has been to identify Christian Stoicism with its unmetamorposized Greek counterpart, much as the West tends to do with Neoplatonism, with the result that genuinely Christian ideas expressed in a particular philosophical medium are simply neglected. Conventionally, the way this argument proceeds is that "Biblical" or "Christian" is set up in opposition to "philosophical" (Neoplatonic, Stoic, etc.). But the fact of the matter is that most any philosophical system can be adapted to Christian use, and every thought "taken captive to Christ," provided that it is Christ that drives the adaptation. Thus it was with Neoplatonism in the East, and thus it is with Stoicism in the West.
To briefly cite some distinctive features of Stoicism that are useful for my purposes, two of the major beliefs included materialism and unity of the soul. The former was the belief that everything was material, so that literally nothing was bodiless (incorporeal). The Stoics accomplished this by modifying the Heracleitean concept of ever-changing fire as the root element. The fundamental substance in Stoicism was pneuma, the combination of air and fire, and it quite well resembled the modern analog: combustion. All of this pneuma pushing matter into collisions, driving it apart, and producing a whole lot of controlled chaos is what made life "go" (following the Heracleitean ethic of constant change and conflict). To explain how pneuma mixed with things, Stoics developed a complicated physics of mixtures, including the concept of a "blending," in which two things remain separable despite being thoroughly permeating with one another (such as water and wine, which can be separated by the use of an oiled sponge). Obviously, this influenced later concepts of the hypostatic union, even though ultimately, the concept of blending as an explanation, proposed by Nestorius, was rejected on account of the inherent separability of the two substances.
The unity of the soul falls in with the Stoic notion that will and rationality were one and the same, leading to the longtime identification with Stoicism as unemotional reaction in the face of circumstances. What is often missed in this account is the crucial importance of the soul being free, providing the entire basis for Stoic ethics. Without that freedom, Stoicism is nothing more than the grim fatalism of paganism bearing with the whims of the gods, something to which Stoicism was prone to degenerate when handled by the careless. This is particularly the case because of the aforementioned materialism; the natural order is established by the divine substance being quite literally in everything, no matter how minute, so that it is quite easy to slip into a mechanistic worldview. But if freedom is preserved in proper Stoic fashion, rationality is a decision, a free choice to behave in coherence with the natural order (and with one's own nature), and indeed, freedom itself is a gift of nature.
The longest Stoic shadow in the West is cast by Quintus Septimius Florens Tertullianus, whom I'll call "Quint" for short, partly because I feel some familarity with him on account of our common occupation and faith and partly because the other name by which he was commonly known has been associated with a large amount of negative press. In fact, I myself didn't think about Quint much, apart from his using a couple of Latin terms that became famous after Nicaea (substantia and persona), but I consider that a grievous oversight. Quint's Christian Stoicism was nothing short of brilliant, exactly because he took every weakness of Stoicism and made it a strength by subverting it for Christian purposes. A good summary may be found in Eric Osborn's Tertullian: First Theologian of the West, but take care not to follow Osborn's denigration of Iamblichean Neoplatonism as irrational "magic," a position which has been convincingly discredited by Gregory Shaw in Theurgy and the Soul.
In Triadology, Quint's Stoic view of everything having a body led him to a pivotal insight about the manifestation of the Word. As Osborn explains, Quint exploited the Stoic distinction between the "inner word" and the "uttered word" to explain that, just as a reasonable man does not refrain from discourse, the Father's inner Word is necessarily uttered. This affirms the monarchy of the Father, as it is in the very nature of the Father to beget (utter) the Son, and the Son as uttered Word conversely serves as the full and entire expression of the Father. Oddly enough, David Bradshaw in Aristotle East and West finds the connection of this concept to Christian doctrine obscure, going so far as to guess that Clement's Stromata might have been an influence on Plotinus. I suspect that this is because he has limited his inquiry to the concept of energeia and neglected that the Stoic doctrine lent itself more naturally to understanding divinity in terms of activity (although having its own difficulties with pantheism).
Likewise, because the Father's substantia is spiritus, it is natural that the Person of the Spirit manifesting the Godhead spiritually ratifies the shared spiritus of the Godhead. At the same time, Quint quite deliberately leaves aside the question of what substantia actually is, and thus he avoids falling into the precarious trap of elementalism and pantheism that beset the Stoics and leaves open the later Neoplatonic solution to the problem of transcendence. In fact, Quint's account of substantia as something like the "defining basis" of a thing is quite creative. He endorses a far broader and less physical concept of substantia, drawing on legal analogies (e.g., a man of "substance" is one of wealth or standing) as well as the more conventional physical analogies so that his idea far outstrips the primitive Stoic/Heracleitean concept.
In addition to preserving the monarchy of the Father, this distinction between the inner Word and the uttered Word also introduces the nature/person distinction meaningfully into the Trinity. Thus, the substantia or quality of the Father and the Son are identical, because the inner Word and the uttered Word both "have" the same content, which is just the divinity/Godhead in its entirety. The only difference between the Father and the Son, therefore, is one of order, aspect, or manifestation (gradus, forma, species), which are personal characteristics. At the same time, it is impossible for the Father to exist without uttering His Word or the Spirit proceeding from Him. This inseparable connection between person and the manifestation of the divine substantia is what inextricably links the economic Trinity to the immanent Trinity.
There's lots more to be said, both about Quint himself as well as his influences and impact. But the lesson here is that Quint's adaptation of Stoicism to Christianity is every bit as original, influential, and yet faithful to Tradition as is the more famous Byzantine adaptation of Neoplatonism. We do a great disservice to Christian history to ignore either of them.