Dynamic theories of anaphora standardly treat negation as externally static, which is inconsistent with anaphora to doubly-negated indefinites, and Partee disjunctions. This work proposes a general technique for lifting dynamic systems into richer meaning spaces that support dynamic negation, and argues that extant theories of dynamic negation instantiate this technique in diļ¬erent ways, varying either the substrate dynamic semantics or the enriched meaning space. As case studies, I show how to improve the empirical predictions of Mandelkern's (2022) 'bounded' theory by swapping out the implicit dynamic substrate, and demonstrate how theories of dynamic negation can benefit from an enriched meaning space that supports exceptional scope for indefinites (Charlow 2024).