We present the design, implementation and evaluation of iVisDesigner, a web-based system that enables users to design information visualizations for complex datasets interactively, without the need for textual programming. Our system achieves high interactive expressiveness through conceptual modularity, covering a broad information visualization design space. iVisDesigner supports the interactive design of interactive visualizations, such as provisioning for responsive graph layouts and different types of brushing and linking interactions. We present the system design and implementation, exemplify it through a variety of illustrative visualization designs and discuss its limitations. A performance analysis and an informal user study are presented to evaluate the system.