BACKGROUND: Clinical variants of primary progressive aphasia (PPA) are diagnosed based on characteristic patterns of language deficits, supported by corresponding neural changes on brain imaging. However, there is (i) considerable phenotypic variability within and between each diagnostic category with partially overlapping profiles of language performance between variants and (ii) accompanying non-linguistic cognitive impairments that may be independent of aphasia magnitude and disease severity. The neurobiological basis of this cognitive-linguistic heterogeneity remains unclear. Understanding the relationship between these variables would improve PPA clinical/research characterisation and strengthen clinical trial and symptomatic treatment design. We address these knowledge gaps using a data-driven transdiagnostic approach to chart cognitive-linguistic differences and their associations with grey/white matter degeneration across multiple PPA variants. METHODS: Forty-seven patients (13 semantic, 15 non-fluent, and 19 logopenic variant PPA) underwent assessment of general cognition, errors on language performance, and structural and diffusion magnetic resonance imaging to index whole-brain grey and white matter changes. Behavioural data were entered into varimax-rotated principal component analyses to derive orthogonal dimensions explaining the majority of cognitive variance. To uncover neural correlates of cognitive heterogeneity, derived components were used as covariates in neuroimaging analyses of grey matter (voxel-based morphometry) and white matter (network-based statistics of structural connectomes). RESULTS: Four behavioural components emerged: general cognition, semantic memory, working memory, and motor speech/phonology. Performance patterns on the latter three principal components were in keeping with each variant's characteristic profile, but with a spectrum rather than categorical distribution across the cohort. General cognitive changes were most marked in logopenic variant PPA. Regardless of clinical diagnosis, general cognitive impairment was associated with inferior/posterior parietal grey/white matter involvement, semantic memory deficits with bilateral anterior temporal grey/white matter changes, working memory impairment with temporoparietal and frontostriatal grey/white matter involvement, and motor speech/phonology deficits with inferior/middle frontal grey matter alterations. CONCLUSIONS: Cognitive-linguistic heterogeneity in PPA closely relates to individual-level variations on multiple behavioural dimensions and grey/white matter degeneration of regions within and beyond the language network. We further show that employment of transdiagnostic approaches may help to understand clinical symptom boundaries and reveal clinical and neural profiles that are shared across categorically defined variants of PPA.