Background. Software sustainability is defined in terms of multiple and interdependent dimensions (economic, social, technical and environmental). Preliminary initiatives have investigated the contribution of certain quality attributes to sustainability dimensions. Problem. Despite these valuable efforts, the characterization of software sustainability is still a key challenge. This entails how sustainability can be embraced in the design of software systems by identifying the relevant software quality attributes (QAs) and their dependencies. Both attributes and dependencies vary heavily with amongst others the type of software system and its operational context. Aim and Method. We followed a multiple case study research method with the main objective of investigating the applicability of the sustainability model in different contexts. We aim also to enrich our model, by means of identifying missing quality attributes or new contributions to the sustainability dimensions. We selected two software projects as cases of our study, where each one was independently conducted in specific situations. Results. The results of the study show that the relevant quality requirements identified in both projects (cases) are covered by most of the QAs related to the social (82%) and technical (83%) dimensions. Moreover, some QAs that were not addressed in the corresponding projects, their relevance like context completeness, and flexibility were acknowledged. These results suggest that the software sustainability model could support the identification of relevant QAs. The case study also contributed to identify QAs that had not been considered in the economic, technical and social dimensions of the sustainability-quality model.