Software quality issues are commonly reported when offshoring software development. Value-based software engineering addresses this by ensuring key stakeholders have a common understanding of quality. Objective: This work seeks to understand the levels of alignment between key stakeholder groups within a company on the priority given to aspects of software quality developed as part of an offshoring relationship. Furthermore, the study aims to identify factors impacting the levels of alignment identified. Method: Three case studies were conducted, with representatives of key stakeholder groups ranking aspects of software quality in a hierarchical cumulative exercise. The results are analysed using Spearman rank correlation coefficients and inertia. The results were discussed with the groups to gain a deeper understanding of the issues impacting alignment. Results: Various levels of alignment were found between the various groups. The reasons for misalignment were found to include cultural factors, control of quality in the development process, short-term versus long-term orientations, understanding of cost-benefits of quality improvements, communication and coordination. Conclusions: The factors that negatively affect alignment can vary greatly between different cases. The work emphasises the need for greater support to align company internal success-critical stakeholder groups in their understanding of quality when offshoring software development.