Co-amorphous drug–drug systems have been developed with the overall aim of improving the physical stability of two or more amorphous drugs. Co-amorphous systems often show good physical stability, and higher solubility and dissolution rates compared to their crystalline counterparts. The aim of this study is to determine if eutectic mixtures of two drugs can form stable co-amorphous systems. Three drug–drug mixtures, indomethacin–naproxen (IND−NAP), nifedipine–paracetamol (NIF−PAR), and paracetamol–celecoxib (PAR−CCX), were investigated for their eutectic and co-amorphization behavior as well as their physical stability in the co-amorphous form. The phase diagrams of the crystalline mixtures and the thermal behavior of the co-amorphous systems were analyzed by differential scanning calorimetry. The solid-state form and physical stability of the co-amorphous systems were analyzed using X-ray powder diffractometry during storage at room temperature at dry conditions. Initial eutectic screening using nifedipine (NIF), paracetamol (PAR), and celecoxib (CCX) indicated that IND−NAP, NIF−PAR, and PAR−CCX can form eutectic mixtures. Phase diagrams were then constructed using theoretical and experimental values. These systems, at different drug-to-drug ratios, were melted and cooled to form binary mixtures. Most mixtures were found to be co-amorphous systems, as they were amorphous and exhibited a single glass transition temperature. The stability study of the co-amorphous systems indicated differences in their physical stability. Comparing the phase diagrams with the physical stability of the co-amorphous mixtures, it was evident that the respective drug–drug ratio that forms the eutectic point also forms the most stable co-amorphous system. The eutectic behavior of drug–drug systems can thus be used to predict drug ratios that form the most stable co-amorphous systems.