We report the synthesis of networks having adjustable topologies and mechanical properties. Our approach consists of photopolymerizing poly(ethylene glycol) diacrylates (PEG-DA) in the presence of mixtures of mono- and multifunctional thiols. We show that the introduction of monothiols as non-cross-linking transfer agents provides a simple way to tune the topology of the networks and produce soft extensible networks. In a systematic study with model short PEG-DA (Mn = 700 g·mol-1), we explored how the gel point and network properties, such as the swelling ratio, the soluble fraction, the viscoelastic moduli, and the ultimate stress and strain, can be adjusted by varying the ratio of thiol to acrylate functions and the average functionality of the thiol mixture. We applied this strategy to longer chains of PEG-DA (Mn = 2300 and 3200 g·mol-1) and varied the viscoelastic and tensile responses of these networks to optimize their adhesive performance. This simple and robust approach further enriches the toolbox of thiol-acrylate polymerization and expands the application scope of PEG-based hydrogels.