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 after the last dose of study therapy

  * Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject
* Within 10 days of treatment registration: Absolute neutrophil count (ANC) \>= 1,500 /mcL
* Within 10 days of treatment registration: Platelets \>= 100,000 / mcL
* Within 10 days of treatment registration: Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment)
* Within 10 days of treatment registration: Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN
* Within 10 days of treatment registration: Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN
* Within 10 days of treatment registration: Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\] =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases
* Within 10 days of treatment registration: Albumin \>= 2.5 mg/dL
* Within 10 days of treatment registration: International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants
* Within 10 days of treatment registration: Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants

Exclusion Criteria:

* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (\> 10 mg of prednisone daily or equivalent steroid doses) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment
* Has a known history of active TB (Bacillus tuberculosis)
* Has hypersensitivity to pembrolizumab or any of its excipients
* Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or has not recovered (i.e. =\< grade 1 or at baseline) from adverse events due to agents administered earlier; Note: Subjects with =\<grade 2 neuropathy are an exception to this criterion and may qualify for the study
* Has received major surgery, subject must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy
* Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability
* Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment
* Has known history of, or any evidence of active, non-infectious pneumonitis
* Has an active infection requiring systemic therapy
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject?s participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment
* Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent
* Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)
* Has known active hepatitis B (e.g. hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g. hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected)
* Has received a live vaccine within 30 days of planned start of study therapy; Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g. Flu-Mist) are live attenuated vaccines, and are not allowed
* Has history of cardiac or pulmonary impairment either by clinical history or symptoms or cardiac ejection fraction \< 40%