Monolingual children tend to assume that a word labels only one object, and this mutual exclusivity supports referent selection and retention of novel words. Bilingual children accept two labels for an object (lexical overlap) for referent selection more than monolingual children, but in these previous studies, information about speakers’ language backgrounds was minimal. We investigated monolingual and bilingual 4-year-old children’s ability to apply mutual exclusivity and lexical overlap flexibly when objects were labelled either by one or two speakers with the same or different language backgrounds. We tested referent selection and retention of word–object mappings. Both language groups performed similarly for mutual exclusivity, were more likely to accept lexical overlap in the two-language than one-language condition, and performance was similar for referent selection and later retention. Monolingual and bilingual children can adapt their word-learning strategies to cope with the demands of different linguistic contexts.