Nothing in the physical world is an appropriate sacrifice to the fully Hypercosmic Gods. This is because they are entirely above the Encosmic Realm and have nothing to do with it or materiality. Instead, immaterial theurgy involves the use of purely spiritual tokens without recourse to physical symbols or ritual. The purpose of immaterial theurgy and unite ourselves with the immaterial Gods. This form of theurgy is rarely practiced and only by the most advanced souls; the Theurgic Sage. This type of theurgy brings about henosis.
Iamblichus, unfortunately, does not tell us how the immaterial sacrifices of purified souls are performed, because those few souls capable of performing them are “superior to all legislation.” However, Gregory Shaw posits a Pythagorean approach to this kind of sacrifice. Given Iamblichus considers himself a Pythagorean, and the fact he sees a direct connection between ritual worship and mathematical practices, Shaw’s idea is credible; after all, Iamblichus considers the Pythagorean decad as identical to the Platonic Forms. Thus, we can conclude that Hypercosmic sacrifices are made through numbers. As each number represents a kind of Form, which is connected to, and come from, the Gods, sacrificing numbers raises the theurgist to the highest divine levels. How exactly these rites are performed is a mystery, but as Proclus relates them to Time and heavenly cycles, they possibly have an astrological component.
Dunn, Patrick. The Practical Art of Divine Magic: Contemporary & Ancient Techniques of Theurgy. Woodbury, MN: Llewellyn Publications, 2015.
Ekklesia Neoplatonismos Theourgia. “Ekklesia Neoplatonismos Theourgia Catechism.” Ekklesia Neoplatonismos Theourgia. Accessed July 17, 2017. http://theourgia.org/catechism/.
Kupperman, Jeffrey S. Living theurgy: a course in Iamblichus philosophy, theology and theurgy. London: Avalonia, 2014.
Shaw, Gregory. Theurgy and the soul: the Neoplatonism of Iamblichus. Second ed. Kettering, OH: Angelico Press, 2014.