General Methodological Notes

What is to be studied in a new metaphysics?#

Metaphysical hierarchy is not morally wrong. There's nothing "morally" wrong about hierarchy. What's wrong is a particular presentation of the hierarchy, which has less to do with the vertical structure of ordering, but with the classification scheme which is static, rigid, and arbitrary due to its extrinsic nature, and the deficiency for this is first and foremost its lack of explanatory power and its complete ignorance of various sectors of reality.
There is a flattening in what is traditionally called "hierarchical arrangement" of the metaphysical order of the universe, so that the intrinsic and the internal of a thing can never be safely probed . The best illustration of this flattening can be found in mathematics.
Euclidean spaces are an image of the architectonic arrangement of traditional metaphysics, while things are manifolds, when seen through the lens of traditional metaphysics, they're embedded through Whitney embedding into a Euclidean space, with their intrinsic characters blurred: properties that comes from the choice of the embedding itself cannot be segregaated from the intrinsic properties of the manifolds. Individualities of manifolds are by construction eschwed.
This so-called hierarchical arrangement, since it is an act of flattening, leads in fact to a reduction or elimination of hierarchical levels. A metaphysics that results in a hierarchiacally arranged account of the universe is also analogous to axiomatic set theory, where a set of axioms are given as the foundations and that all mathematical propositions are put in the same level. In Zermelo-Fraenkel set theory, the Hahn-Banach theorem and the proposition \(1+1=2\) are in the same hierarchical level, thus even if the former is self-evident and can be proved in \(\mathsf{RCA}_0\) and the latter is an elaborate theorem which cannot be proved in \(\mathsf{RCA}_0\) but needs \(\mathsf{WKL}_0\), there is nothing that accounts for this difference of strength needed for them to hold in Zermelo-Fraenkel set theory.
Now it might be argued that thus a metaphysics that takes the so-called multiplicity (or even "diversity") that is said to be inherently present in the world into account, but it is quite clear that there's nothing inherently good in taking account of the so-called multiplicity. A metaphysics makes sense of the world, but making sense is relative to an end. But at the same time an end can be an end that is genuinely defined only in so far as it is made sense in a metaphysics. This ourboros of meaning rests upon an elusive foundation that can never be grasped in its totality by intellect since that very act of grasping it alters the ground: the ground itself is dynamic. We may, instead, want to traverse the orthogonal path, and inquiry into the way metaphysics works, that is to say, it is not a particular schema for categorization, or worse, classification, that is relevant, even the rationale for this schema isn't that which is essential, but the mechanism of schema-generation. 
This may lead to an infinite regress: what's the mechanism of the inquiry into the mechanism of schema-generation? But from the from of the regression we can see that this regression is a fixed point that only looks like a dynamic regression. There's no content added in an attempt to answer the question that is posed in a higher level of regression than in a lower level, hence the whole infinite sequence, since it is predictably generated, can be finitely subsumed under a single operation of regression.

Avoid Lip-service metaphysics#

By this I mean those varieties of metaphysics that posits, for example, a reality that is a "field of energies", and saying that whatever things are condensation of these "energies", and so on. There's zero content in these sorts of metaphysics that I'm always perplexed by the fact that majority of humanity are quite pleased by them.
Metaphysics is not any "ground" or "premise", while sometimes it may seem so, especially when the order that is under question pertains to exposition, or a general coherence, rather than thought-genesis. Metaphysics is that which emerges when a thoughts constellate. In one direction it is meta- in the modern sense of meta-, namely, it is the condensation of experience of the so-called transcendental, in other direction it is meta- in the sense of "post", since the experience of transcendence is mediated and embodied by the concrete. Thus it is a highly compact subject that encodes the, say, mechanism of schema-generation, of the mystery of genesis, which tries to capture the intrinsic. It is not 1.a sweeping account of the fundamental nature of things given in the form of formulas, but 2. an account of formula-generating mechanism.
An example should illustrate the difference between 1. and 2. That which underlies geometric logic is obviously more metaphysical than a particular formal definition of a logical system. The former cannot be formulated, but the principle is omnipresent and all-encompassing. The latter can be formulated, and while it is universal in its own schematization of everything, it flattens.