This work presents an extension of the projector operator embedding scheme of Manby et al. [J. Chem. Theory Comput. 8, 2564 (2012)] in a multicomponent (MC) framework. Here, a molecular system containing electrons and other types of quantum species is divided into a wavefunction (WF) subsystem of interest and a density functional theory (DFT) environment. The WF-in-DFT partition decreases computational costs by partially truncating the WF subsystem basis set at the cost of introducing a controllable embedding error. To explore the applicability of the MC extension, third-order propagator-in-DFT calculations were performed for positron–anion complexes for alkoxides and carboxylates with carbon chains of different sizes. For these systems, it was found that selecting a WF subsystem with the positron and only the oxygen atoms caused an error of 0.1 eV or lower in positron-binding energies, while reducing between 33% and 55% the basis set size. The reduction of computational costs achieved with the embedding scheme allowed us to improve molecular positron-binding energy predictions by performing complete basis set limit extrapolations. Combining the WF-in-DFT embedding and the complete basis set extrapolation, positronium aliphatic alkoxides were predicted to be energetically stable by 0.3 eV with respect to Ps emission. Similarly, positronium carboxylates, both aromatic and aliphatic, were predicted to be stable by 1.3 eV.