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It is widely accepted that most natural language terms do not have precise universally agreed definitions that fix their meanings. Instead, humans use terms in a variety of ways that adapt to different contexts and points of view. In this paper we present a framework based on Supervaluation Semantics for interpreting languages in the presence of semantic variability. This work builds on supervaluationist accounts, which explain linguistic indeterminacy in terms of a collection of possible precise interpretations of the terms of the language. We extend the basic supervaluation semantics by adding the notion of standpoint. A multi-modal logical language for describing standpoints is presented. The language includes a modal operator ⬜s for each standpoint s, such that ⬜s φ means that proposition φ is unequivocally true according to standpoint s — i.e. φ is true at all precisifications compatible with s. We show how it can be used to represent logical properties and connections between alternative ways of describing a domain and different accounts of the semantics of terms.