This study investigates the structural behavior of a representative reinforced concrete (RC) framed module from a larger building constructed in the 1960s–1970s within the ILVA industrial complex in Bagnoli (Naples, Italy). The module consists of two RC frames connected transversely only by the slab, a common structural configuration of that period, typically lacking seismic design provisions. Pushover analyses were performed to assess the module’s performance both in its original state and after retrofitting with an innovative seismic energy dissipation system, known as Resisto 5.9. This system is a lightweight steel exoskeleton made of cold-formed steel profiles, reinforced with diagonal cross bracing. This system enhances lateral strength and energy dissipation while also supporting thermal insulation panels, thereby improving both seismic resilience and energy efficiency. The numerical model was calibrated and validated using experimental data, with particular focus on foundation connection scenarios—comparing the performance of anchored versus unanchored exoskeleton configurations. Results showed significant improvements in shear strength, lateral stiffness, and ultimate displacement capacity, especially when the exoskeleton is anchored. These findings highlighted the potential of steel exoskeleton retrofitting as an effective and minimally invasive method to enhance the seismic resilience of aging RC buildings.