Head and neck squamous cell carcinomas (HNSCCs) are a complex group of malignancies that affect different body sites pertaining to the oral cavity, pharynx and larynx. Current chemotherapy relies on platinum complexes, the major exponent being cisplatin, which exert severe side effects that can negatively affect prognosis. For this reason, other metal complexes with less severe side effects are being investigated as alternatives or adjuvants to platinum complexes. In this context, exploiting (supra)additive effects by the concurrent administration of cisplatin and emerging metal complexes is a promising research strategy that may lead to effective cancer management with reduced adverse reactions. Here, the combined action of cisplatin and a ruthenium(II) η6-arene compound (RuCy), both as free molecules and loaded into hybrid nano-architectures (NAs), has been assessed on HPV-negative HNSCC models of increasing complexity: 2D cell cultures, 3D multicellular tumor spheroids, and chorioallantoic membranes (CAMs). Two new NAs have been established to explore all the delivery combinations and compare their ability to enhance the efficacy of cisplatin in the treatment of HNSCCs. A significant supra-additive effect has been observed in both 2D and 3D models by one combination of treatments, suggesting that cisplatin is particularly effective when loaded on NAs, whereas RuCy performs better when administered as a free compound. Overall, this work paves the way for the establishment of the next co-chemotherapeutic approaches for the management of HNSCCs.