Microfluidic hanging-drop networks enable culturing and analysis of 3D microtissue spheroids derived from different cell types under controlled perfusion and investigating inter-tissue communication in multi-tissue formats. In this paper we introduce a compact on-chip pumping approach for flow control in hanging-drop networks. The pump includes one pneumatic chamber located directly above one of the hanging drops and uses the surface tension at the liquid-air-interface for flow actuation. Control of the pneumatic protocol provides a wide range of unidirectional pulsatile and continuous flow profiles. With the proposed concept several independent hanging-drop networks can be operated in parallel with only one single pneumatic actuation line at high fidelity. Closed-loop medium circulation between different organ models for multi-tissue formats and multiple simultaneous assays in parallel are possible. Finally, we implemented a real-time feedback control-loop of the pump actuation based on the beating of a human iPS-derived cardiac microtissue cultured in the same system. This configuration allows for simulating physiological effects on the heart and their impact on flow circulation between the organ models on chip.