Two rather attractive aspects of Trinitarian theology are perichoresis (the continual pouring out of love for each other by the three Hypostases) and coinherence (a term that originally referred to the dual human and divine nature of Christ, but can also be used to refer to a panentheist worldview of 'God in all and all in God', and can also mean the way all three Persons of the Trinity reside in each other). If it is then assumed that the Divine permeates all of creation, we should therefore expect to see this threefold pattern repeated everywhere, including the human soul - as above, so below. Certainly it is possible to discern threefoldness (inner, outer, and inter for example) in many ways of perceiving reality - but there are other numerical symbols of the unfolding of the Divine into creation. So it would be unwise to dismiss Trinitarian theology completely; there is much that is worthwhile in it - but it is not the sole truth. Here's an alchemical post on Unurthed that looks at the Duality, Triplicity, Quaternity and the Quintessence. Note how the alchemist emphasises prayer as the basis of alchemical work.
Perichoresis (the continual mutual flow of love) is linked to kenosis (the pouring out of self in order to be filled with the Divine, which bestows true Selfhood). For some, this is linked to the contemplative life (which necessarily results in compassion for others and love of nature); for others, it is fulfilled in the paths of action or devotion. All three of these paths lead to Tifereth and ultimately to the source.