MP is notoriously difficult to define. But I think that seeing MP as a stack of layers may help.

1. MP as clarified physics.
2. MP as whatever sense of “being” survives self-critical epistemology. (Cf. The epistemological turn, which made knowing prior to being—which is reasonable, since the only being that MP can discuss is the being it can discursively access.)
3. MP as framework (and formalism) of conceptual preconditions for thinking physics.
4. MP as arguments showing the nature of ultimate substance. Popular candidates include matter, mind, God, undifferentiated consciousness, neutral monism, apeiron, nothing, bottomless processual flows, and pure formal relations.
5. After Heidegger, we should also include “the total lifeworld situation that gives rise to human organisms asking the question of being-as-such”—which is just philosophical common sense fortified with sprinkles of historicism and awareness that meaning and pertinency are social emergents. Cf. Foucault’s discursive practices, or the processes through which (dominant) reality comes into being, which emphasis on the plasticity of such “reality” and the unfortunate role of power in determining it.

But my favorite definition is one that makes MP totally unique and magical. From Britannica —

It thus seems that the assertion that a special science like mathematics is uncritical about its archai is false; there is a sense in which mathematicians are constantly strengthening their basic premises. As regards the corresponding claim about metaphysics, it has at one time or another been widely believed (1) that it is the business of metaphysics to justify the ultimate assumptions of the sciences, and (2) that in metaphysics alone there are no unjustified assumptions.

Concerning (1), the question that needs to be asked is how the justification is supposed to take place. It has been argued that the metaphysician might, on one interpretation of his function, be said to offer some defense of science generally by placing it in relation to other forms of experience. To do this, however, is not to justify any particular scientific assumptions. In point of fact, particular scientific assumptions get their justification, if anywhere, when a move is made from a narrower to a more comprehensive science; what is assumed in geology, for example, may be proved in physics. But this, of course, has nothing to do with metaphysics.

The difficulty with (2) is that of knowing how any intellectual activity, however carefully conducted, could be free of basic assumptions. Some metaphysicians (such as Bradley and his Scottish predecessor J.F. Ferrier) have claimed that there is a difference between their discipline and others insofar as metaphysical propositions alone are self-reinstating. For example, the Cartesian proposition cogito, ergo sum (“I think, therefore I am”) is self-reinstating: deny that you think, and in so doing you think; deny that you exist, and the very fact gives proof of your existence. Even if it could be made out that propositions of this kind are peculiar to metaphysics, however, it would not follow that everything in metaphysics has this character. The truth is, rather, that no paradox is involved in denying most fundamental metaphysical claims, such as the assertion of the Materialist that there is nothing that cannot be satisfactorily explained in material terms or the corresponding principle of Aristotle that there is nothing that does not serve some purpose.

This is the most exciting definition of MP, and the most exciting idea in all of philosophy, whose heart is the Rationalist dream of seeing to the ground of being by means of a transparent procedure that constructs it.