 It is fairly straightforward to develop formal languages and theories of higher-level plural quantification (Rayo 2006). For instance, we can introduce variables of the form xxx to be thought of as ranging over second-level pluralities and the relation \(xx \prec_2\) xxx to be understood in analogy with the relation \(x \prec xx\). (See Linnebo and Rayo 2012 for extensions to transfinite levels and comparison of the resulting theories with those of ordinary set theory.) But can these formal theories of higher-level plural quantification be justified by considerations similar to those that justify the theories PFO and PFO+?