Task-oriented dialogue systems employ third-party APIs to serve end-users via natural language interactions. While existing advances in Natural Language Processing (NLP) and Machine Learning (ML) techniques have produced promising and useful results to recognize user intents, the synthesis of API calls to support a broad range of potentially complex user intents is still largely a manual and costly process. In this paper, we propose a new approach to recognize and realize complex user intents. Our approach relies on a new rule-based technique that leverages both (i) natural language features extracted using existing NLP and ML techniques and (ii) contextual knowledge to capture the different classes of complex intents. We devise a context knowledge service to capture the requisite contextual knowledge.