On the Boundary between Material and Formal Ontology

There are two main ways, philosophically, of characterizing the business of ontology. On one account, made popular by Quine, ontology is concerned with the material question of what there is. On the other, which made its way into our times through Brentano and his pupils, ontology is concerned with the task of laying bare the formal structure of all there is, whatever it is. My question, here, is whether one can pursue one sort of theory without also engaging in the other—whether, or to what extent, the tasks of material ontology presuppose the backing of some formal-ontological theory, and whether or to what extent formal ontology can be, in the material sense of the term, ontologically neutral.