Query evaluation over Linked Data sources has become a complex story, given the multitude of algorithms and techniques for single- and multi-source querying, as well as the heterogeneity of Web interfaces through which data is published online. Today's query processors are insufficiently adaptable to test multiple query engine aspects in combination, such as evaluating the performance of a certain join algorithm over a federation of heterogeneous interfaces. The Semantic Web research community is in need of a flexible query engine that allows plugging in new components such as different algorithms, new or experimental SPARQL features, and support for new Web interfaces. We designed and developed a Web-friendly and modular meta query engine called Comunica that meets these specifications. In this article, we introduce this query engine and explain the architectural choices behind its design. We show how its modular nature makes it an ideal research platform for investigating new kinds of Linked Data interfaces and querying algorithms. Comunica facilitates the development, testing, and evaluation of new query processing capabilities, both in isolation and in combination with others.