Many philosophers are attracted to fine-grained accounts of properties, propositions, and relations (PPRs). The structuralist view, asserting that PPRs are built up by their constituents, has gained increasing attention over recent decades. However, it has been argued that the Russell-Myhill paradox shows the inconsistency of this view within higher-order logic. In response, I propose a stage theory in which structured entities are iteratively generated, thereby preventing the paradox from arising. In this approach, the whole universe of PPRs is never available, but rather it indefinitely expands across the hierarchy of stages. In particular, my proposal suggests a predicative turn of higher-order logic, contending that if the generation of PPRs in stages is taken seriously, it necessitates the restriction of quantification to entities available at each particular stage of the generative process.