The global plastic waste crisis remains a fundamental challenge for mankind to address, as vast amounts of plastic continue to accumulate in the environment, threatening ecosystems and human health. Biobased and biodegradable plastics, particularly materials based on aliphatic polyesters, offer a promising alternative to conventional non-degradable, petroleum-based polyolefins, but typically suffer from inferior thermomechanical performance. To comply with existing industrial processing techniques, such as blow molding or film drawing, these sustainable materials must be modified to exhibit sufficiently high melt strength and melt extensibility. In this context, polymers bearing end groups capable of supramolecular aggregation are particularly promising. Recent studies on high-molar-mass oligopeptide-modified polymers have shown that these materials exhibit rubber-like behavior and strain hardening in the polymer melt when blended them with additives that boost supramolecular motif concentration. This enables melt drawing to high draw ratios and the fabrication of highly oriented films. The present thesis investigates the dependence of this behavior on the deformation rate, the supramolecular motif and its concentration, and the molecular-scale network dynamics by using 1,3,5-benzenetricarboxamide (BTA) as a supramolecular motif in view of its reliable self-assembly into nanofibrils, comparatively high transition temperatures, and industrial relevance. For a representative aliphatic polyester, we demonstrate that BTA-based polymer end groups efficiently co-assemble with an additive into nanofibrils that serve multiple functions. They are highly efficient nucleating agents for the crystallization of the polyester matrix, and form supramolecular networks that give rise to a high-melt-strength rubbery regime extending to temperatures of up to 149 °C. The melt behavior under large tensile deformations, such as during film melt drawing, is governed by the competition between polymer chain stretching and relaxation processes, which are modulated by the supramolecular network dynamics. Using nuclear magnetic resonance spectroscopy, we establish a site-specific, non-destructive method to determine molecular scale dissociation rate constants for the nanofibrils in the bulk melt. Applying this technique, we show that BTA-based networks exhibit faster molecular-scale dissociation kinetics than oligopeptide-based materials. Consequently, despite their higher dissociation temperatures, melts containing BTA-based networks fail via viscous flow at strain rates and temperatures where oligopeptide-based blends remain extensible and display pronounced strain hardening. However, blending polyesters modified with BTA-based end groups with 1 wt% of a chiral BTA analogue yields aggregates with significantly slower exchange dynamics, resulting in strain hardening and dramatic improvements in melt extensibility (up to 3200%). Films produced by melt-drawing of such blends are optically transparent and exhibit a highly oriented "shish-kebab" morphology. This work demonstrates that tuning the dynamics of supramolecular networks is a key design principle for enabling large-strain processability in high-molar-mass supramolecular polymer materials. Our strategy is applicable to other polymer types and may facilitate the fabrication of oriented materials from sustainable polymers for many important applications, including barrier films, foams, and food packaging.