Pembro and HER2Bi-Armed Activated T Cells in Treating Patients With Metastatic Castration Resistant Prostate Cancer

PRIMARY OBJECTIVES: I. To estimate the clinical efficacy of 8 infusions of HER2 HER2Bi-armed activated T cells (BATs) (up to 10\^10/infusion) twice per week for 4 weeks in combination with pembrolizumab once every 3 weeks starting with one dose 3 weeks before the 1st BATs infusion, by assessing the percentage of patients free of clinical progression at 6 months after registration. SECONDARY OBJECTIVES: I. Evaluate phenotype, cytokine profiles and IFN-gamma enzyme-linked immunosorbent spots (ELISpots), cytotoxicity and antibodies directed at laboratory prostate cancer cell lines for proof of principle of immune system activation and to correlate with clinical outcomes of response, progression free survival (PFS), and overall survival (OS). II. Evaluate the magnitude of change in tumor infiltrating T cells, PD-1 expression, and the Th1/Th2 ratio in prostate cancer tumor tissue before and after immunotherapy and correlate it with the clinical outcomes of response, PFS, and OS. OUTLINE: Patients receive pembrolizumab intravenously (IV) over 30 minutes every 3 weeks. Treatment repeats every 3 weeks for up to 6 months in the absence of disease progression or unacceptable toxicity. Beginning at least 1 week after pembrolizumab, patients receive HER2Bi-armed activated T cells IV over 5-15 minutes 2 times a week for 4 weeks in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months.