Supplements have often been characterized as inert with respect to other content. But under closer scrutiny, the data shows that supplements can take scope and participate in anaphoric links, undermining multidimensional accounts of them. I argue that the core empirical facts pertaining to supplements, including projection, can in many cases be accounted for by more general, independently motivated factors such as anaphora resolution in discourse and quantifier scope preferences. Importantly, supplement projection is decoupled from at-issueness, with projection arising instead as an epiphenomenon of various external influences.The account is formalized in a dynamic, compositional, and unidimensional semantics that allows anaphoric links to and from supplement content. Since supplements are modeled as a kind of quantifier phrase modifier, scope interactions with semantic operators are captured without further stipulation. When a supplement takes widest scope, it constitutes a separate at-issue proposal, enabling both supplement projection and (non)deniability. The formal machinery requires no additional rules or representation layers except for the dynamic meaning of the comma intonation, which demarcates a supplement from its surrounding content.