Evaluating Immune Therapy, Duravalumab (MEDI4736) With Tremelimumab for Relapsed/Refractory Germ Cell Tumors

Inclusion Criteria: * Age ≥ 18 years at time of informed consent * Body weight \> 30 kg * Histologically confirmed diagnosis of GCT (nonseminoma or seminoma in men; non-dysgerminomas, dysgerminomas, or germinomas in women or patients with pineal gland GCT) at MSKCC of any primary site (includes female GCT and intracranial GCT). * Evidence of measurable disease either by RECIST 1.1 or elevation of serum tumor markers (AFP \> 15 ng/mL or HCG \>2.2 mIU/ml). * Patients must have progressed after at least one prior systemic therapy for GCT and meet one of the following criteria: a. Patients with evidence of progressive or recurrent GCT after progression prior high dose chemotherapy (HDCT) treatment, defined as meeting at least on of the following criteria: i. Tumor biopsy of new or growing or unresectable lesions demonstrating viable GCT. In the event of an incomplete gross resection where viable GCT is found, patients will be considered eligible for this study. ii. Consecutive elevated serum tumor markers (HCG or AFP) that are increasing. Increase of an elevated LDH alone does not constitute progressive disease. iii. Development of new or enlarging lesions in the the setting of persistently elevated HCG or AFP, even if the HCG and AFP are not continuing to rise. b. Patients deemed not to be a candidate for or benefit from potentially curative HDCT or other curative treatment options defined as follows: i. Patients with inadequate renal function for HDCT. ii. Patients who h…