It seems as if debates about divine natures, among the "laity," are usually preoccupied with what have been called first-order properties of those natures. So we see the perennial quibbling over naive definitions of "omniscience" or "omnipotence." But philosophically sensitive (or informed) theologians often appeal to higher-order divine properties more essentially:
Upon the question, which attribute is to be considered primary, opinions differ. Many eminent theologians favour the conception of pure actuality (Actus Purus), from which simplicity and infinity are directly deduced. Most modern authors fix on aseity (Aseitas; a = "from" se = "himself"), or self-existence; for the reason that, while all other existences are derived from, and depend on, God, He possesses in Himself, absolutely and independently, the entire reason of His uncaused infinite Being. In this, the most profound and comprehensive distinction between the Divinity and everything else, all other distinctions are implicitly expressed. Whether, and in what way, the distinctions between the attributes and the metaphysical essence, and among the attributes themselves have an ontological basis in the Divine nature itself was subject which divided Nominalists and Realists, Thomists and Scotists, in the age of Scholasticism (cf. Vacant, Dict. de théol. cathol., I, 2230-34).
... God’s simplicity is a second-order property, that is, a property of God’s first-order properties such as wisdom, power, goodness, and the like. The doctrine of simplicity may entail that God’s (real) first-order properties are identical. But does it entail that all of God’s (real) second-order properties are identical with his (real) first order properties (and thus that God’s simplicity is identical with whatever first-order properties suffice for identity with God)? It isn’t clear that it does. Since simplicity and other divine second-order properties supervene on his first-order properties, the latter entail the former; nothing could instantiate each of God’s (real) first-order properties without instantiating such properties as simplicity. But the converse may not be true. For couldn’t a thing be simple in the defined sense (namely, having all its first-order real properties identical with each other and with its being) without having the divine properties? (Numbers might be an example.) If it could, then simplicity is not identical with the real first-order properties that suffice to make God God.
Does the Old Testament assume a hierarchy of properties arranged according to order? First-order properties and relations would be those that can only be instantiated by YHWH qua individual. For example, being spiritual can be instantiated by YHWH and other spiritual entities and phenomena. But the Old Testament does not assume that the property of spirit is itself a spirit, it only exists as a trope (in the metaphysical sense as the-spiritual nature-of-something/somebody). It is natural to suppose, however, that at least many first-order properties and relations can themselves have properties and relations. Here again we might think of YHWH’s property of divinity (e.g. generic godhood). Thus the property of YHWH’s divinity was thought to exemplify the property of being a type of entity. And of course, once we think of second-order properties for YHWH, it is natural to wonder whether there are third-order properties (properties of second- or, perhaps in cumulative fashion, of second- and first-order properties), and so on up through ever-higher orders.
Question: suppose that a divine being had first-order properties like (presumably) maxipotence (not omnipotence, for which the prefix "omni-" causes so much trouble) and It had those as "generated" by logical deduction from a second-order basis like (presumably) simplicity. However, does this being then have the third-order property sustains the distinction between first- and second-order properties? And so on and on: but if It does, would this conflict with the point of attributing simplicity to the divine nature? Have we reintroduced unlimited plurality into the divine essence by differentiating Its properties in such a way as by appealing to distinctions in order? One might say, "Yes, we have pluralized the divine nature infinitely, but this is still not a plurality that is incompatible with the simplicitarianism intended beforehand," but is simplicitarianism a useful thesis if it is compatible with infinite, abstract multiplicity accruing to an "absolute" monad?