 Already Lupher &amp; Kronz (2005) point out that an attractive alternative to the strict \(C^{\ast}\)-algebraic imperialism is to extend the physical content to von Neumann algebras, the elements of which are generated by representations of algebra \(\mathcal{A}\). Lupher (2018) analyzes the algebraic imperialists’ use of Fell’s theorem in detail and points out that there are important representations in the algebraic approach to which Fell’s theorem does not apply, in particular many \(W^{\ast}\)-algebras, the abstract counterparts of von Neumann algebras. Moreover, he argues that it is a \(W^{\ast}\)-algebra, namely the bidual \(\mathcal{A}^{\ast \ast}\), which is the appropriate locus of physical content for the algebraic imperialist, to which Lupher subscribes in the form of what he dubs “bidualism.” One crucial advantage of taking the \(W^{\ast}\)-algebra \(\mathcal{A}^{\ast \ast}\) is that it is larger than the \(C^{\ast}\)-algebra \(\mathcal{A}\). In particular it also contains what Ruetsche (2011) calls “parochial observables” (or the abstract counterparts thereof), such as net magnetization and particle number. Also against Ruetsche, Feintzeig (2018) argues that not only the universalist (or bidualist) but also \(C^{\ast}\)-algebraic imperialism has access to “parochial observables,” since it has additional tools to represent such observables by means of idealizations from the observables in the abstract algebra.