Local metaphysics or local naturalism is a relatively recent term used by some pragmatically inclined analytic philosophers (e.g. Cahoone and Whimsatt), who trace their lineage to the classical pragmatism of Peirce, Dewey and Mead. It is somewhat close in spirit to the ontological positions of the older Stanford Disunity Mafia, like Nancy Cartwright's and Dupré's, who did not use the label. Ross, whose monograph is linked in the OP, is a critic. The localization of metaphysics parallels the localization of the one true Logic of old into multiple modern logics serving different purposes, see What are the differences between philosophies presupposing one Logic versus many logics?
To the "global" metaphysics of old, that attempted to present a unified picture of how the world is, local metaphysics contrasts a pragmatic plurality of ontologies servicing different subject fields: for dispositions, causal powers, moral values, abstract objects, quantum objects, events, parts and wholes, personal identity, etc. Even incompatible ontologies for the same subject are acceptable as long as they serve legitimate and complementary purposes. All of them are treated as fallible and revisable, and the task of integration is deferred to indefinite future. Yet, these plural ontologies are intended to capture the truth of things at their limited levels, and remain effectively valid to a point even when subsumed by more comprehensive versions, like geometric and wave optics by modern electrodynamics.
Here is from Cahoone's A Kind of Naturalism that reads like a manifesto:
"I ask only what ontology would explain and be justified by our most reliable explanatory practices, rather than offering hypotheses aiming to integrate all of our intellectual hopes. Peirce once said that a critic had written that he, Peirce, did not seem entirely certain of his own conclusions. Peirce regarded that as great praise...
To this old-fashioned fallibilism we may make two additions. First, we shall drop any significant talk about the putative endpoints of inquiry, the most comprehensive (the Whole), the most invariant (the Highest), the most elementary (Simples), or the most fundamental (Foundations). To know these endpoints we would have to know something significant about everything, which we should not expect to be able to do. Our hope is to know important features of indefinitely many things. We are rejecting globalism, the belief that what something is, or our knowledge of it, hangs on the most inclusive order in which it functions. Democritus’s Atomism, Plato’s idealism of forms, Descartes’s dualism, Hegel’s idealism of spirit, and Quine’s physicalism are all globalist.
A local metaphysics does not hold knowledge of more robust orders hostage to knowledge of the most inclusive orders. Inquiry into a subject matter’s smallest components or widest environment has no ontological priority; we start with a metaphysics of the middle, with the scales of reality we know most robustly, then move outward in all directions. It is, after all, knowledge of the more robust orders against which guesses about the less robustly known will be tested. One might say localism aims to capture realities at levels of description that tend to remain invariant across differing global metaphysical descriptions."