Plastic pollution has recently emerged as a major global environmental problem, especially during the global pandemic. The problem spans land, ocean, and air pollution via macro-, micro-, and nanoplastics. Despite the availability of different technologies for recycling plastics under a Circular Economy, their deployment has been hampered by challenges stemming from socio-economic factors. For example, poor segregation of waste by consumers leads to cross-contamination of plastic streams that have recovery potential. Although the enhancement of Plastics Recycling Networks (PRNs) is clearly needed, little progress has been achieved worldwide. In this work, a new class of Process Integration (PI) approaches are developed for optimal planning of PRNs. These approaches draw on the proven capabilities of PI for effective decision support. The basic PRN synthesis problem is defined by a set of sources (waste plastic streams) and sinks (recycling plants) using a systems approach. All streams are assumed to consist of a mix of recyclable polymer and non-recyclable contaminants. Each recycling plant has a predefined processing capacity and upper limit on the contaminant level in its feed stream. Graphical Pinch Analysis (PA) is proposed for this PRN synthesis problem. A scenario-based case study where 95.5% of the available waste is recycled demonstrates its practical application. Prospects for future extensions of the PRN synthesis problem are also discussed.