In several publications, a theoretical basis for a universal data model has been proposed, but its practical implementation has been considered only at the level of a general preliminary sketch. Many questions remain open, which complicates the creation of real systems implementing this model. In particular, the issue of processing queries to data presented in various traditional data models and stored in a system based on a universal data model has not been studied. The purpose of the study is to develop a method for implementing a system for processing queries to data presented in various traditional models and jointly stored in a universal data model as well as to develop the architecture of such a query processing system. The article presents the results of an analysis of existing query handlers to assess the possibility of their use and proposes a method for integrating query handlers in MDX, SQL, and Cypher into a single data management system based on an archigraph DBMS. An architecture is presented that allows unifying access and query processing to heterogeneous data, such as relational tables, multidimensional cubes, vertices, and edges of property graphs. The results obtained were used in developing the first prototype of the system. This opens prospects for further development and implementation of the universal data model and its varieties in various information systems, improving their flexibility and efficiency.