(1) Background: Precision oncology is opening new treatment opportunities for patients suffering from solid tumors. In the last two decades, the advent of CDK4/6 inhibitors, immunotherapy, and antibody–drug conjugates (ADC) improved survival outcomes for advanced or metastatic breast cancers (BC). Nevertheless, some patients progress to approved therapies and still maintain good clinical conditions. (2) Methods: With the aim to estimate the accrual rate to experimental precision oncology treatments, we collected molecular and clinical characteristics of BC patients evaluated at Phase 1 Unit of Fondazione Policlinico Gemelli. Clinical data were retrieved from hospital records. Molecular analysis was performed using Next-Generation Sequencing (NGS) FoundationOne CDx on tissue or blood. (3) Results: Among the 38 BC patients referred to our unit, 35 completed the genomic analysis. All patients were female with advanced (mean number of metastatic sites: 3, range 1–6) BC. Median age at our evaluation was 52 (IQR, 48–59). ECOG PS was good in 97% of the study population, although heavily pre-treated (median number of systemic treatments: 5, IQR 3–7). Half of referred patients were HR+/HER2− BC, with 39% triple negative breast cancer (TNBC). NGS testing was performed on relapsed disease among most (71%) participants, in particular lymph nodes and soft tissue. Liquid biopsy was requested in 23% of cases. The median time from sample collection to NGS testing was 1 month and from diagnosis 54 months. The median value of mutations, VUS, and TMB were 6, 11, and 5, respectively. TP53, PIK3CA, BRCA2, ESR1, and RAD21 were the genes with the highest number of molecular alterations. In 5 patients (14%), the molecular analysis was helpful to assign targeted therapy in the context of clinical trials with a median progression-free survival of 5 months. (4) Conclusions: HR+/HER2− and TNBC were the most frequent subtypes referred for NGS testing. Tissue biopsy of relapsed disease was feasible in 71% of cases. The molecular analysis offered a new treatment opportunity in 14% of patients. The real benefit of these treatments remains to be evaluated in larger cohorts.