Circular economy approaches are commonly depicted by two cycles, where the biological cycle is associated with regeneration in the biosphere and the technical cycle with reuse, refurbishment, and recycling to maintain value and maximize material recovery. This work, instead, presents an alternative vision to the management of carbon-based materials that integrates the two cycles and enables the phasing-out of fossil carbon from the material system. The aim is to investigate the benefits and global potential of a co-recycling system, as an alternative to conventional recycling systems that separate biomass-based materials (e.g., wood, paper) from fossil-based materials (e.g., plastics).