Unlocking the full potential of Knowledge Graphs (KGs) to enable or enhance various semantic and other applications requires Data Management Systems (DMSs) to efficiently store and process the content of KGs. However, the increases in the size and variety of KG datasets as well as the growing diversity of KG queries pose efficiency challenges for the current generation of DMSs to the extent that the performance of representative DMSs tends to vary significantly across diverse query types and no single platform dominates performance. We present our extensible prototype, SymphonyDB, as an approach to addressing this problem based on a polyglot model of query processing as part of a multi-database system supported by a unified access layer that can analyze/translate individual queries just-in-time and match each to the likely best-performing DMS among Virtuoso, Blazegraph, RDF-3X, and MongoDB as representative DMSs that are included in our prototype at this time. The results of our experiments with the prototype over well-known KG benchmark datasets and queries point to the efficiency and consistency of its performance across different query types and datasets.