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Ontology-based data access is an emerging yet powerful technology that allows to enhance a classical relational database with an ontology in order to infer new intensional knowledge. Recently, Datalog+/- was introduced with the purpose of providing tractable reasoning algorithms for expressive ontology languages. In this framework, Datalog is extended by features such as existential quantification in rule heads, and at the same time the rule syntax is restricted to guarantee decidability, and also tractability, of relevant reasoning tasks. In this paper, we enrich Datalog even more by allowing not only existential quantification but also disjunction in rule heads, and we investigate the complexity of reasoning under the obtained formalism.