Integration of multiple three-dimensional microtissues into microfluidic networks enables new insights in how different organs or tissues of an organism interact. Here, we present a platform that extends the hanging-drop technology, used for multi-cellular spheroid formation, to multifunctional complex microfluidic networks. Engineered as completely open, 'hanging' microfluidic system at the bottom of a substrate, the platform features high flexibility in microtissue arrangements and interconnections, while fabrication is simple and operation robust. Multiple spheroids of different cell types are formed in parallel on the same platform; the different tissues are then connected in physiological order for multi-tissue experiments through reconfiguration of the fluidic network. Liquid flow is precisely controlled through the hanging drops, which enable nutrient supply, substance dosage and inter-organ metabolic communication. The possibility to perform parallelized microtissue formation on the same chip that is subsequently used for complex multi-tissue experiments renders the developed platform a promising technology for 'body-on-a-chip'-related research.