Highly functional biobased epoxy resins were prepared using dipentaerythritol (DPE), tripentaerythritol (TPE), and sucrose as core polyols that were substituted with epoxidized soybean oil fatty acids, and the impact of structure and functionality of the core polyol on the properties of the macromolecular resins and their epoxy-anhydride thermosets was explored. The chemical structures, functional groups, molecular weights, and compositions of epoxies were characterized using nuclear magnetic resonance (NMR) spectroscopy, Fourier-transform infrared (FTIR) spectroscopy, gel permeation chromatography (GPC), and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI MS). The epoxies were also studied for their bulk viscosity, intrinsic viscosity, and density. Crosslinked with dodecenyl succinic anhydride (DDSA), epoxy-anhydride thermosets were evaluated using differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), tensile tests, and tests of coating properties. Epoxidized soybean oil (ESO) was used as a control. Overall, the sucrose-based thermosets exhibited the highest moduli, having the most rigid and ductile performance while maintaining the highest biobased content. DPE/TPE-based thermosets showed modestly better thermosetting performance than the control ESO thermoset.