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Cloud-based software applications (Software as a Service - SaaS) for multi-tenant provisioning have become a major development paradigm in Web engineering. Instead of serving a single end-user, a multi-tenant SaaS provides multiple end-users with the same functionality but with potentially different quality-of-service (QoS) values. The service selection for such a SaaS is a complex decision-making process which involves a number of stakeholders with different QoS requirements. SaaS developers need to compose services with different QoS values to meet end-users' different multidimensional QoS constraints for the SaaS. Furthermore, they also need to satisfy SaaS providers' optimisation goals for the SaaS, such as least resource cost and best system performance. Existing QoS-aware service selection approaches are oriented at a single tenant. They do not consider the characteristics of multi-tenant SaaS and hence are ineffective and inefficient when applied to compose multi-tenant SaaS. In this paper, we introduce a novel QoS-driven approach for helping SaaS developers select the services for composing multi-tenant SaaS, which achieves SaaS providers' optimisation goals while fulfilling the end-users' different levels of QoS constraints. The proposed approach is evaluated using an example SaaS synthetically generated based on a dataset of real-world Web services. Experimental results show that our approach significantly outperforms existing approaches in terms of both effectiveness and performance.