 One way of going beyond PFO+ would be by allowing quantification into predicate positions, including those of predicates taking plural arguments. Doing so would result in an extension which stands to PFO+ as ordinary (singular) second-order logic stands to ordinary (singular) first-order logic. Such extensions will not be considered here: for whether they are legitimate, and if so what axioms they may support, has less to do with plurals and plural quantification than it does with predication and quantification over the semantic values of  predicates.[11]