The plastic waste crisis is among humanity’s most urgent challenges. However, widespread adoption of sustainable plastics is hindered by their often inadequate processing characteristics and performance. Here, we introduce a bio-inspired strategy for the modification of a representative high molar mass, biodegradable aliphatic polyester that helps overcome these limitations and remains effective at molar masses far greater than the entanglement molar mass. We use co-assembly of oligopeptide-based polymer end groups and a low molar mass additive to create a hierarchical structure characterized by regularly spaced nanofibrils interconnected by entangled polymer segments. The modified materials show a rubbery plateau at temperatures above their melting point, associated with strongly increased melt strength, extraordinary melt extensibility, improved dimensional stability, and accelerated crystallization. These thermomechanical property changes open up otherwise inaccessible processing routes and offer considerable scope for improving solid-state properties, thereby addressing typical shortcomings of sustainable alternatives to conventional plastics.