Language learning and use relies on both domain-specific and domain-general cognitive and sensory-motor functions. Evolutionary and developmental perspectives, as well as the use of language in interaction, suggest an overlap between language and other skills. Building on our previous behavioural findings, which outlined a consistent behavioural association between language and domain-general skills, we investigated brain-behavioural associations using story listening during fMRI and behavioural measures of language, reading, multilingual experience, cognition, musicality, arithmetic, and motor skills. Participants varied in multilingual language experience and reading aptitudes, including both typical (TRs) and dyslexic readers (DRs). Using multivariate Partial Least Squares correlation, we identified a main component linking cognitive, linguistic, and phonological measures to brain areas underlying lexico/semantics, combinatorial processing, and amodal semantic processing. A second analysis excluding DRs showed closer associations between cognitive/linguistic, literacy, phonological and memory processes within the same brain network as in the full sample. Here, we also isolated additional, complementary components, including one involving speed, automatization and lexical access, linked to auditory and motor brain areas. This suggests greater coherence and more integrated, 'expert' processing in TRs. This work is a first step in exploring complex relationships between language and non-linguistic functions that are important to it.