Quine was generally rather nominal than realistic towards the relative abstract within the context of a predicate as described here. A predicate is a sentence that contains a finite number of quantified variables range over non-logical objects and becomes a statement when specific values are substituted for the variables.
And of such entities Quine canvassed an influential mistrust: a mistrust based, initially,
on their mere abstractness—though Quine himself later, under pressure of the apparent needs of
science, overcame his phobia of the abstract—but also on the ground that they seem to lack clear
criteria of identity—a clear basis on which they may be identified and distinguished among
themselves. It was the latter consideration which first led Quine to propose that the range of the
variables in higher-order logic might as well be taken to be sets—abstract identities no doubt, but
ones with a clear criterion of identity given by the axiom of extensionality—and then eventually to
slide into a view in which "second-order logic" became, in effect, a misnomer—unless, at any
rate, one regards set theory as logic.
Followers of Hilbert have continued to quantify predicate letters, obtaining what they call
higher-order predicate calculus. The values of these variables are in effect sets; and this
way of presenting set theory gives it a deceptive resemblance to logic .... set theory's
staggering existential assumptions are cunningly hidden now in the tacit shift from
schematic predicate letters to quantifiable set variables.
So as you rightly concerned, later Quine allowed sets (including abstract properties such as whiteness, elephanthood, etc) as variables in a predicate sentence but mainly in higher-order logic. In strict and classic FOL, variables should remain as concrete objects to keep its "first order only" simplicity in a formal way.
A natural language sentence involving (abstract) properties as relative adjective such as "There is a white dog." cannot be strictly expressed in FOL simply as ∃d in D White(d) ∧ Dog(d), since predicate adjectives are not the exactly same kind of thing as second-order predicates such as color.
Btw, here's another source confirming Quine's anti-realistic view about his ontological commitment:
Ontological parsimony can be defined in various ways, and often is equated to versions of Occam's razor, a "rule of thumb, which obliges us to favor theories or hypotheses that make the fewest unwarranted, or ad hoc, assumptions about the data from which they are derived." Glock regards 'ontological parsimony' as one of the 'five main points' of Quine's conception of ontology.
FOL is a framework in which one can only quantify over elements of the domain of discourse. In second-order logic one is allowed to quantify over subsets of the domain of discourse. If you really want to substitute a set value ({dog A, dogB, dog C}) to a quantified variable in FOL with same nominal level (easy situations), modern plural quantification (per Boolos 1984 and Lewis 1991) is the theory that an individual variable x may take on plural, it can give FOL the power of set theory, but without any "ontological commitment" to such objects as sets in line with Quine's view (bear in mind ultimately logic wants to avoid set theory and be free of set related paradoxes).
