SaaS (Software-as-a-Service) often uses multi-tenancy architecture (MTA) where tenant developers compose their applications online using the components stored in the SaaS database. Tenant applications need to be tested, and combinatorial testing can be used. While numerous combinatorial testing techniques are available, most of them produce static sequences of test configurations and their goal is often to provide sufficient coverage such as 2-way interaction coverage. But the goal of SaaS testing is to identify those compositions that are faulty for tenant applications. This paper proposes an adaptive test configuration generation algorithm AR (Adaptive Reasoning) that can rapidly identify those faulty combinations so that those faulty combinations cannot be selected by tenant developers for composition. The AR algorithm has been evaluated by both simulation and real experimentation using a MTA SaaS sample running on GAE (Google App Engine). Both the simulation and experiment showed show that the AR algorithm can identify those faulty combinations rapidly. Whenever a new component is submitted to the SaaS database, the AR algorithm can be applied so that any faulty interactions with new components can be identified to continue to support future tenant applications.