A claim management office (CMO) is a new intra-organisation fit based on an organisational project management (OPM) approach and deals specifically with improving claim performance. However, CMOs are either misunderstood or often overlooked in construction companies, mainly due to ignorance of the OPM context but further exacerbated by a lack of real case study research on how to adopt CMOs in these organisations. To address this knowledge gap, this present study integrates organisational ambidexterity with X-inefficiency theory (due to organisation intra-firm irrational decisions when managing such claims) to generate a reference framework for the CMO by probing its implementation within an international construction firm. A multi-method approach, including a single case study (a firm which adopted a CMO) and internal and external expert panels, was used for sampling, data collection, analysis and validation of the framework. The reference framework provides new perspectives on how construction-related companies and practitioners can adopt a CMO structure, which enables them to improve claims performance by planning in three interrelated activities, viz. function-, process- and performance-based. Theoretically, findings also contribute to the X-inefficiency and organisational ambidexterity theories, specifically, how different influences among the reference framework’s elements lead to better organisational claim performance as a plausible roadmap for future work.