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

Inclusion Criteria: * Be willing and able to provide written informed consent/assent for the trial * Have histologically confirmed prostate adenocarcinoma, with metastases * Progression by either PSA, Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria for measurable disease or new areas of metastases on bone scan or symptom progression related to prostate cancer despite castrate levels of testosterone; (level \< 50 ng/ml) * Be agreeable to continue to maintain castrate levels of testosterone * At least 2 weeks should have elapsed since any immunosuppressive therapy * At least 4 weeks since prior chemotherapy for metastatic disease or at least 2 weeks since prior androgen targeting agents such as ketoconazole, abiraterone, enzalutamide, etc. * Discontinue anti-androgens prior to therapy; at least 6 weeks since last dose of bicalutamide or nilutamide and at least 4 weeks from last dose of flutamide * Have normal bone marrow, renal and hepatic function as deemed by the treating physician and approved by the clinical principal investigator (PI) Dr. Vaishampayan * Not have concurrent anti-cancer therapy * Not have concurrent immunosuppressive therapy or medical condition likely to cause immunosuppression * Have life expectancy \> 6 months * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)/Zubrod performance scale * Agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days aft…