With impressive density and coding capacity, DNA offers a promising solution for building long-lasting data archival storage systems. In recent implementations, data retrieval such as random access typically relies on a large library of non-interacting PCR primers. While several algorithms automate the primer design process, the capacity and scalability of DNA-based storage systems are still fundamentally limited by the availability of experimentally validated orthogonal primers. In this work, we combine the nested and semi-nested PCR techniques to virtually enforce multidimensional data organization in large DNA storage systems. The strategy effectively pushes the limit of DNA storage capacity and reduces the number of primers needed for efficient random access from very large address space. Specifically, our design requires * unique primers to index $ data entries, where specifies the number of dimensions and indicates the number of data entries stored in each dimension. We strategically leverage forward/reverse primer pairs from the same or different address layers to virtually specify and maintain data retrievals in the form of rows, columns, tables, and blocks with respect to the original storage pool. This architecture enables various random-access patterns that could be tailored to preserve the underlying data structures and relations (e.g., files and folders) within the storage content. With just one or two rounds of PCR, specific data subsets or individual datum from the large multidimensional storage can be selectively enriched for simple extraction by gel electrophoresis or readout via sequencing.