Standard first-order logic interprets reference, predication and quantification in terms of fixed denotations with respect to a domain of precise objects. We explore ways to generalise this semantics to account for variability of meaning due to factors such as vagueness, context and diversity of definitions or opinions. We present Variable Reference Logic (VRL), an elaboration of Standpoint Logic, which is a multi-modal logic based on a variety of Supervaluation Semantics. VRL can accommodate several modes of variability in relation to both predicates and objects. Its principal novelty is that its semantics incorporates a domain of indefinite individuals, whose precise properties (such as spatial extension) are not fully determinate. Each indefinite individual is associated with a set of precise entities corresponding to possible precise versions of the individual.