NoSQL systems support new data models, which propose alternative models to the well-known relational models, and query languages. Due to the lack of a well-accepted logical model for Data Warehouses (DWs), some preliminaries works proposes extensions/redefinition of relational star and snow-flake schemata for NoSQL families. However, many other modeling possibilities remain unexplored, and it is difficult to compare these proposals because of the lack of a well-recognized benchmarking framework for DWs. In this paper, we propose a generic extension of the relational Star Schema Benchmark, called GenSSB, to handle any kind of DBMS in terms of logical models. We validate our framework by instantiating GenSSB for some different logical models and DBMSs