The mechanism of assembly of the extracellular matrix protein fibronectin (FN) into elastic, insoluble fibrils is still poorly understood. FN fibrillogenesis requires cell-generated forces, which expose cryptic FN-FN binding sites buried in FN Type III domains. The number and location of cryptic binding sites have been debated, but experimental evidence suggests multiple domains may contain FN-FN binding sites. The requirement of cell-dependent forces to generate FN fibrils restricts investigation of the mechanism of assembly. To address this, we use a recently developed biophysical model of fibrillogenesis to test competing hypotheses for the location and number of cryptic FN-FN binding sites and quantify the effect of these molecular alterations on assembled FN fibril properties. Simulations predict that a single FN-FN binding site facilitates either negligible fibrillogenesis or produces FN fibrils that are neither robust nor physiological. However, inclusion of multiple FN-FN binding sites predicts robust fibrillogenesis, which minimally depends on individual domain properties. Multiple FN-FN binding site models predict a heterogeneous fibril population that contains two distinct phenotypes with unique viscoelastic properties, which we speculate may play a key role in generating heterogeneous mechanical signaling in the extracellular matrix of developing and regenerating tissues.