A study has been carried out of binary solid systems made up of the antiepileptic drug levetiracetam, LEV, and a nonsteroidal anti-inflammatory drug, NSAID, capable of managing the inflammation that accompanies epileptic activity. One aim of this research was to identify eutectic mixtures and co-crystals, which are able to impact positively on their biopharmaceutical properties. The NSAIDs studied are (S)- and (R,S)-ibuprofen, (S)- and (R,S)-naproxen, (R,S)-ketoprofen and (R,S)-flurbiprofen, all class II in the Biopharmaceutical Classification System. A green mechanochemical methodology has been used to prepare binary mixtures with different molar ratios, and the binary solid-liquid phase diagrams established. For LEV + (S)-ibuprofen, formation of a single (1:1) co-crystal was confirmed; this was found to melt incongruently. The co-crystal was found to be stable in accelerated stability tests. For the other systems, interesting eutectic mixtures were identified, which showed enhanced dissolution rates of the NSAID relative to the pure drug. For LEV + (R,S)-ibuprofen, LEV + (S)-naproxen and LEV + (R,S)-naproxen, the eutectic mixture compositions have the effective doses of both components. All the NSAIDs investigated are chiral, and their racemates are racemic compounds. Levetiracetam, the (S)-enantiomer of etiracetam, was not efficient in enantiomer discrimination, as all the racemic compound structures are present as the prepared solid mixtures.