Durvalumab and Standard Chemotherapy Before Surgery in Treating Patients With Variant Histology Bladder Cancer

PRIMARY OBJECTIVES: I. To assess the safety and tolerability of durvalumab in combination with chemotherapy in subjects with variant histology bladder cancer. SECONDARY OBJECTIVES: I. To determine the percent of subjects post-neoadjuvant chemo-immunotherapy who achieve tumor stage of pT2 N0 M0 or better (pT1 N0 or pT0) at cystectomy. II. To assess the response rate (RR) in post-neoadjuvant chemo immunotherapy as assessed by the investigator using imaging at screening and post treatment. III. To assess the molecular characterization of tumor tissue pre-neoadjuvant therapy and at post treatment cystectomy (for subject who have persistent disease). IV. To determine circulating free deoxyribonucleic acid (DNA) (cfDNA) (cell free DNA) at baseline, during treatment and following post treatment cystectomy using Natera sequencing platform. OUTLINE: Patients are assigned to 1 of 3 cohorts. COHORT I: Patients receive durvalumab intravenously (IV) over 60 minutes on day 1. Chemotherapeutic agents will be administered as an IV infusion according to prescribing information or treatment guidance in general use by the Investigating site. Methotrexate on day 1, vinblastine IV on day 2, doxorubicin IV on day 2, and cisplatin IV on day 2. Cycles repeat every 14 days up to 4 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo cystectomy within 6 weeks. COHORT II: Patients receive durvalumab IV over 60 minutes on day 1. Chemotherapeutic agents will be administered as an IV infusion according to prescribing information or treatment guidance in general use by the Investigating site. Cisplatin IV over 60 minutes on day 1, and gemcitabine IV on days 1 and 8. Cycles repeat every 21 days up to 4 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo cystectomy within 6 weeks. COHORT III: Patients receive durvalumab IV over 60 minutes on day 1.Chemotherapeutic agents will be administered as an IV infusion according to prescribing information or treatment guidance in general use by the Investigating site. Carboplatin IV on day 1, and gemcitabine IV on days 1 and 8. Cycles repeat every 21 days up to 4 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo cystectomy within 6 weeks. After surgery, patients are followed up at 30 and 90 days.