Broadly speaking, the Brandomian critique of claims of two-stage models of representation — where representings are sharply distinguished from representeds, as supposedly having immediate intelligibility that representeds lack — seems to me to have at least a partial analogue in early Derrida’s critique of presence and of what he called a transcendental signified, as well as to some of what Foucault wrote about representation in The Order of Things.
Brandom does not want to entirely subvert representation, as Derrida and Foucault sometimes seemed to. He just wants to insist that it is always derivative, and cannot be a starting point. Although Derrida was less anti-Hegelian than many of his contemporaries, I don’t recall that he recognized, as Brandom does, that there was a strong precedent for the critique of immediacy/presence in Kant and Hegel. Foucault‘s very sharp overt rejection of Hegel needs to be balanced against the fact that his own historical account of what are in effect shapes of subjectivity covers many of the same moments as Hegel’s, and in effect strongly continues the Hegelian critique of Mastery.
Unfortunately, Brandom sees both Foucault and Derrida as meriting no more than one-line dismissals, where I see common ground in the critiques of mastery, immediacy, and representation. These days, Brandom’s more rationalist and ethical version of these critiques seems a good deal more useful to me, but I still prefer a more irenic attitude. (See also Genealogy.)
Brandom is bothered by Derrida’s thesis that signifiers technically refer to other signifiers that refer to other signifiers, and so on, without end. While I agree that an indefinite expansion of inferences is more perspicuous than an indefinite expansion of references, Brandom’s explanation of reference in terms of inference ought to make it possible to substitute the one for the other. Also, the notion of a signifier is very abstract; we should not equate signifiers with individual words, which Brandom also seems to do in this context. A signifier could be a complex expression. Thinking about substitution of complex expressions makes it easier to map expansions of references to expansions of inferences. I think the indefinite deferral of a “transcendental signified” should also be related to the Kantian indefinite deferral of claims about things in themselves, and to the Kantian thesis that transcendental concepts do not refer to objects.