Designing yield stress fluids to exhibit desired functional properties is an integral challenge in many applications such as 3D printing, drilling, food formulation, fiber spinning, adhesives, and injectable biomaterials. Extensibility in particular has been found to be a highly beneficial characteristic for materials in these applications; however, few highly extensible, high water content materials have been reported to date. Herein we engineer a class of high water content nanocomposite hydrogel materials leveraging multivalent, noncovalent, polymer-nanoparticle (PNP) interactions between modified cellulose polymers and biodegradable nanoparticles. We show that modulation of the chemical composition of the PNP hydrogels controls the dynamic cross-linking interactions within the polymer network and directly impacts yielding and viscoelastic responses. These materials can be engineered to stretch up to 2000% strain and occupy an unprecedented property regime for extensible yield stress fluids. Moreover, a dimensional analysis of the relationships between extensibility and the relaxation and recovery time scales of these nanocomposite hydrogels uncovers generalizable design criteria that will be critical for future development of extensible materials.