Background/Objectives: The use of intravenous immunoglobulins enriched with IgA and IgM (eIg) in patients with septic shock remains controversial due to a lack of robust, standardized criteria for patient selection and the timing of treatment. This study introduces the SORRISO Score, which is a novel, evidence-informed scoring system designed to guide clinical decision-making for the administration of eIg. Methods: Based on data from the Italian multicentric SORRISO registry, involving 248 patients across seven ICUs from 2015 to 2022, the score integrates patient-related and therapy-related variables. These were derived through an enhanced version of the TO-PIRO Score and include factors such as immunosuppressive status, infection type, timing of treatment, and adequacy of antibiotic therapy. Results: Statistical analyses, including Kaplan–Meier curves and regression models, identified the key predictors of survival and validated the score’s ability to stratify patients by outcome. A cutoff of 13.7 showed a significant prognostic value (AUC = 0.731), with lower scores correlating with increased mortality. Conclusions: The SORRISO Score thus offers a practical bedside tool for improving patient selection for eIg therapy, potentially optimizing outcomes in septic shock; however, it should be validated in a larger cohort of patients.