In the last decade, many business applications have moved into the cloud. In particular, the "database-as-a-service" paradigm has become mainstream. While existing multi-tenant data management systems focus on single-tenant query processing, we believe that it is time to rethink how queries can be processed across multiple tenants in such a way that we do not only gain more valuable insights, but also at minimal cost. As we will argue in this paper, standard SQL semantics are insufficient to process cross-tenant queries in an unambiguous way, which is why existing systems use other, expensive means like ETL or data integration. We first propose MTSQL, a set of extensions to standard SQL, which fixes the ambiguity problem. Next, we present MTBase, a query processing middleware that efficiently processes MTSQL on top of SQL. As we will see, there is a canonical, provably correct, rewrite algorithm from MTSQL to SQL, which may however result in poor query execution performance, even on high-performance database products. We further show that with carefully-designed optimizations, execution times can be reduced in such ways that the difference to single-tenant queries becomes marginal.