This work reports for the first time the copolymerization studies of 11 newly synthesized epoxidized vegetable oils (EVOs) that reacted with a disulfide-based aromatic dicarboxylic acid (DCA) to produce thermoset materials with recyclability properties. These new EVOs' reactivity and properties were compared with those of the two commercial references: epoxidized linseed oil (ELO) and epoxidized soybean oil (ESO). The structure-reactivity correlation is proposed by differential scanning calorimetry (DSC) analysis, corroborating the epoxy content of EVO monomers, the initiator effect, the copolymerization reaction enthalpy, and the temperature range. The thermomechanical properties of the obtained thermosets were evaluated and discussed in correlation with the structure and reactivity of monomers by dynamic mechanical analysis (DMA), tensile testing, and thermogravimetric analysis (TGA). It has been found that the higher the EVO functionality, the higher is the reactivity, cross-linking density, and final performances, with tan δ values ranging from 34 to 111 °C. This study investigates the chemical recycling and the solvent resistance of these vitrimer-like materials that have a high bio-based carbon content, from 58 to 79%, with potential application in coating or composite materials in the automotive sector.