A series of materials was prepared by curing acrylated epoxidized soybean oil (AESO) and dibutyl itaconate (DBI) or ethyl cinnamate (EC) comonomers to provide examples of thermosets with a high proportion of bio-based carbon, in accordance with the principles of green chemistry. The comonomers, representative of cellulose-derived (DBI) or potentially lignin-derived (EC) raw materials, were tested at levels of 25%, 33%, and 50% by mass and the resulting products were characterized by infrared spectroscopy, thermogravimetric analysis, and dynamic mechanical analysis. Both DBI and EC were incorporated into the thermosets to a high extent (>90%) at all concentrations tested. The AESO-DBI and AESO-EC blends showed substantial degradation at 390–400 °C, similar to pure AESO. Glass transition temperatures decreased as comonomer content increased; the highest Tg of 41.4 °C was observed for AESO-EC (3:1) and the lowest Tg of 1.4 °C was observed for AESO-DBI (1:1). Accordingly, at 30 °C the storage modulus values were highest for AESO-EC (3:1, 37.0 MPa) and lowest for AESO-DBI (1:1, 1.5 MPa).