In this paper, we formulate a new problem for any account of Free
Choice (FC) inferences, which we dub FC with anaphora. According to the classical FC inference schema, given a sentence of the form ♢(φ ∨ ψ), one can infer ♢φ and ♢ψ. FC with anaphora involves cases where an anaphoric dependency spans φ ∨ ψ. Anaphora is heavily constrained in disjunctions, but a negative existential statement in the initial disjunct can license a pronoun in the latter disjunct — so called bathroom disjunctions, e.g., “Either there’s no bathroom in this house, or it’s in a funny place”. We show that embedding a bathroom disjunction under an existential modal gives rise to a FC inference that doesn’t follow from the classical schema — since the schema is stated in terms of the individual disjuncts, any information about anaphoric dependencies between disjuncts is lost. In order to capture FC with anaphora, we develop a semantic account based on Goldstein 2019, couched in the framework of Bilateral Update Semantics. We also discuss alternative ways of accounting for FC with anaphora, within an exhaustification framework, as well as introducing several related problems involving anaphora and inferences which we characterize as involving simplification more generally.