Defect-free fully coordinated (FC) structures are well known to be highly stable for a number of materials exhibiting three-coordinated bonding at the nanoscale (e.g., C60) . For topologically more complex nanosystems with higher bonding connectivities the structures and stabilities of the lowest energy FC structures with respect to low-energy defective isomers are unknown. Herein, we describe a general method to thoroughly search through the low-energy geometries of only those nanoclusters that possess FC atomic connectivities. As a pertinent example of our approach we investigate four-connected SiO2, a fundamentally important network-forming material used in many applications at the nanoscale. Using our method we predict that a structurally complex stability crossover from defective to FC nanoclusters occurs in SiO2 at a size of ~100 atoms. At variance with previous works, based on constructing FC SiO2 cagelike nanoclusters by hand, we also show that cagelike clusters are only favored for smaller cluster sizes with dense FC topologies becoming energetically favored with increasing system size.