The oxidation of biogenically emitted volatile organic compounds (BVOC) plays an important role in the formation of secondary organic aerosols (SOA) in the atmosphere. Peroxy radicals (RO2) are central intermediates in the BVOC oxidation process. Under clean (low-NOx) conditions, the main bimolecular sink reactions for RO2 are with the hydroperoxy radical (HO2) and with other RO2 radicals. Especially for small RO2, the RO2 + HO2 reaction mainly leads to closed-shell hydroperoxide products. However, there exist other known RO2 + HO2 and RO2 + RO2 reaction channels that can recycle radicals and oxidants in the atmosphere, potentially leading to lower-volatility products and enhancing SOA formation. In this work, we present a thermodynamic overview of two such reactions: (a) RO2 + HO2 -> RO + OH + O-2 and (b) R'O-2 + RO2 -> R'O + RO + O-2 for selected monoterpene + oxidant derived peroxy radicals. The monoterpenes considered are alpha-pinene, beta-pinene, limonene, trans-beta-ocimene, and Delta(3)-carene. The oxidants considered are the hydroxyl radical (OH), the nitrate radical (NO3), and ozone (O-3). The reaction Gibbs energies were calculated at the DLPNO-CCSD(T)/def2-QZVPP//omega B97X-D/aug-cc-pVTZ level of theory. All reactions studied here were found to be exergonic in terms of Gibbs energy. On the basis of a comparison with previous mechanistic studies, we predict that reaction a and reaction b are likely to be most important for first-generation peroxy radicals from O-3 oxidation (especially for beta-pinene), while being less so for most first-generation peroxy radicals from OH and NO3 oxidation. This is because both reactions are comparatively more exergonic for the O-3 oxidized systems than their OH and NO3 oxidized counterparts. Our results indicate that bimolecular reactions of certain complex RO, may contribute to an increase in radical and oxidant recycling under high HO2 conditions in the atmosphere, which can potentially enhance SOA formation.