The multi-junction concept is the most relevant approach to overcome the Shockley-Queisser limit for single-junction photovoltaic cells. The record efficiencies of several types of solar technologies are held by series-connected tandem configurations. However, the stringent current-matching criterion presents primarily a material challenge and permanently requires developing and processing novel semiconductors with desired bandgaps and thicknesses. Here we report a generic concept to alleviate this limitation. By integrating series- and parallel-interconnections into a triple-junction configuration, we find significantly relaxed material selection and current-matching constraints. To illustrate the versatile applicability of the proposed triple-junction concept, organic and organic-inorganic hybrid triple-junction solar cells are constructed by printing methods. High fill factors up to 68% without resistive losses are achieved for both organic and hybrid triple-junction devices. Series/parallel triple-junction cells with organic, as well as perovskite-based subcells may become a key technology to further advance the efficiency roadmap of the existing photovoltaic technologies.