In 1981 Kaufmann proved the set-theoretic analogue of a result due to Paris and Kirby in the context of arithmetic that connects fragments of the collection scheme to the existence of proper partially elementary end extensions. In particular, he shows that a countable resolvable model of a weak set theory has a proper \(\Sigma_{n+1}\)-elementary end extension if and only if it satisfies collection for all \(\Pi_n\)-formulae. In the same paper Kaufmann asks if every \(L_\alpha\) (the \(\alpha\)-th level of Goedel’s constructible hierarchy) that has a proper \(\Sigma_2\)-elementary end extension necessarily has one that satisfies bounded collection. Clote (1983) asks a generalised version of Kaufmann’s question for models of fragments of PA: Does every countable model of \(B\Sigma_{n+2}\) have a proper \(\Sigma_{n+2}\) elementary end extension that satisfies \(B\Sigma_{n+1}\)? Sun Mengzhou has recently (2025) shown that Clote’s question has a positive answer. In this talk I will describe recent work showing that, in contrast, the set-theoretic analogue of Clote’s question (the generalisation of Kaufmann’s original question) has a negative answer