Co-amorphous drug amino acid mixtures were previously shown to be a promising approach to create physically stable amorphous systems with the improved dissolution properties of poorly water-soluble drugs. The aim of this work was to expand the co-amorphous drug amino acid mixture approach by combining the model drug, naproxen (NAP), with an amino acid to physically stabilize the co-amorphous system (tryptophan, TRP, or arginine, ARG) and a second highly soluble amino acid (proline, PRO) for an additional improvement of the dissolution rate. Co-amorphous drug-amino acid blends were prepared by ball milling and investigated for solid state characteristics, stability and the dissolution rate enhancement of NAP. All co-amorphous mixtures were stable at room temperature and 40 °C for a minimum of 84 days. PRO acted as a stabilizer for the co-amorphous system, including NAP–TRP, through enhancing the molecular interactions in the form of hydrogen bonds between all three components in the mixture. A salt formation between the acidic drug, NAP, and the basic amino acid, ARG, was found in co-amorphous NAP–ARG. In comparison to crystalline NAP, binary NAP–TRP and NAP–ARG, it could be shown that the highly soluble amino acid, PRO, improved the dissolution rate of NAP from the ternary co-amorphous systems in combination with either TRP or ARG. In conclusion, both the solubility of the amino acid and potential interactions between the molecules are critical parameters to consider in the development of co-amorphous formulations.