In the face of grand challenges like global warming or social inequality, firms are increasingly expected to make a positive contribution to society. As a result, they are looking for ways to fuse their own and common good interests, for example, by employing so-called Common Good HRM practices. These practices like the promotion of a constructive error management culture (EMC) aim to support an environment that facilitates positive societal and ecological change by enabling firm leaders and employees to contribute to global progress. Yet, to date empirical evidence for proposed positive effects is scarce and the embeddedness of employees in different teams and national cultures is largely neglected in prior research. The current study accounts for these shortcomings by investigating the effects of a constructive EMC as a Common Good HRM practice on employee innovativeness and internal corporate social responsibility (CSR) based on a sample of 82,927 employees working in 9253 teams in a large telecommunication company with subsidiaries in 10 different countries. Applying a comprehensive multi-level design, we find that (i) a constructive EMC has a positive impact on employee innovativeness and internal CSR and (ii) that team member diversity regarding gender, age, and tenure and cultural values affect EMC. Particularly, our analyses uncover that EMC effects differ depending on the kind of diversity and reveal a complex interplay of team composition and cultural values. Despite notable limitations like the examination of only one single organization, our work underpins the theoretically proposed benefits of applying Common Good HRM practices and highlights the need to take both team and cultural influences into account.