We previously proposed a paradigm shift in genomic data management, based on the Genomic Data Model (GDM) for mediating existing data formats and on the GenoMetric Query Language (GMQL) for supporting, at a high level of abstraction, data extraction and the most common data-driven computations required by tertiary data analysis of Next Generation Sequencing datasets. Here, we present a new GMQL-based system with enhanced accessibility, portability, scalability and performance. The new system has a well-designed modular architecture featuring: (i) an intermediate representation supporting many different implementations (including Spark, Flink and SciDB); (ii) a high-level technology-independent repository abstraction, supporting different repository technologies (e.g., local file system, Hadoop File System, database or others); (iii) several system interfaces, including a user-friendly Web-based interface, a Web Service interface, and a programmatic interface for Python language. Biological use case examples, using public ENCODE, Roadmap Epigenomics and TCGA datasets, demonstrate the relevance of our work. The GMQL system is freely available for non-commercial use as open source project at: http://www.bioinformatics.deib.polimi.it/GMQLsystem/. Supplementary data are available at Bioinformatics online.