Inclusion Criteria:

          -  Histologically confirmed diagnosis of prostate cancer (adenocarcinoma of the prostate)

          -  Metastatic disease as evidenced by the presence of soft tissue and/or bone metastases
             on imaging studies (CT of abdomen/pelvis, bone scintigraphy)

          -  Castrate-resistant disease, defined as follows:

               -  All participants must have received (and be receiving) standard of care androgen
                  deprivation treatment (surgical castration versus GnRH analogue or antagonist
                  treatment); subjects receiving Gonadotropin-releasing hormone (GnRH) analogue or
                  antagonist must continue this treatment throughout the time on this study.

               -  Participants may or may not have been treated previously with a nonsteroidal
                  antiandrogen. For participants previously treated with an antiandrogen, they must
                  be off use of anti-androgen for at least 4 weeks (for flutamide, apalutamide, or
                  enzalutamide) or 6 weeks (for bicalutamide or nilutamide) prior to registration.
                  Moreover, participants who demonstrate an anti-androgen withdrawal response,
                  defined as a > 25% decline in PSA within 4-6 week of stopping a nonsteroidal
                  antiandrogen, are not eligible until the PSA rises above the nadir observed after
                  antiandrogen withdrawal.

               -  Participants must have a castrate serum level of testosterone (< 50 ng/dL) within
                  6 weeks of day 1

          -  Progressive disease while receiving androgen deprivation therapy defined by any one of
             the following as per the Prostate Cancer Clinical Trials Working Group 3 (PCWG3) bone
             scan criteria or RECIST 1.1 during or after completing last therapy:

               -  PSA: At least two consecutive rises in serum PSA, obtained at a minimum of 1-week
                  intervals, with the final value > 2.0 ng/mL.

               -  Measurable disease: > 50% increase in the sum of the cross products of all
                  measurable lesions or the development of new measurable lesions. The short axis
                  of a target lymph node must be at least 15 mm by spiral CT to be considered a
                  target lesion

               -  Non-measurable (bone) disease: The appearance of two or more new areas of uptake
                  on bone scan (or Sodium Fluoride (NaF) positron emission tomography-computed
                  tomography (PET/CT)) consistent with metastatic disease compared to previous
                  imaging during castration therapy. The increased uptake of pre-existing lesions
                  on bone scan will not be taken to constitute progression, and ambiguous results
                  must be confirmed by other imaging modalities (e.g. X-ray, CT or MRI).

          -  Prior treatment with abiraterone or enzalutamide is permitted, but participants must
             have weaned to a daily corticosteroid dose equivalent of no more than 5 mg prednisone
             daily for at least 28 days prior to day 1.

          -  Life expectancy of at least 6 months

          -  Participants must have an Eastern Cooperative Oncology Group (ECOG) performance status
             of 0, 1, or 2.

          -  Adequate hematologic, renal, liver, and coagulation function as evidenced by the
             following within 6 weeks of day 1:

               -  White Blood Cells (WBC) > 2000 / mm3

               -  Absolute Neutrophil Count (ANC) > 1500 / mm3

               -  Hemoglobin (HgB) > 9.0 gm/dL

               -  Platelets > 100,000 / mm3

               -  Creatinine < 1.5 x institutional upper limit of normal (ULN)

               -  Total bilirubin < 1.5 x institutional ULN OR direct bilirubin < ULN for
                  participants with total bilirubin levels > 1.5 x ULN

               -  Aspartate Aminotransferase (AST),Alanine Aminotransferase (ALT) < 2.5 x
                  institutional upper limit of normal

               -  Prothrombin Time (PT) or International Normalized Ratio (INR) < 1.5 x ULN unless
                  participant is receiving anticoagulant therapy and PT is within therapeutic range
                  of intended use of anticoagulant (only required for participants receiving
                  biopsy)

               -  Partial Thromboplastin Time (PTT) < 1.5 x ULN unless participant is receiving
                  anticoagulant therapy and a PTT is within therapeutic range of intended use of
                  anticoagulant (only required for participants receiving biopsy)

          -  No known history of human immunodeficiency viruses (HIV 1 and 2), Human T-cell
             leukemia virus type 1 (HTLV-1), or active Hepatitis B or Hepatitis C

          -  Participants must be at least 4 weeks from any prior treatments and have recovered (to
             < Grade 2) from acute toxicity attributed to this prior treatment, unless considered
             chronic

          -  A subset of participants (6 participants per treatment arm) treated at the lead
             University of Wisconsin (UW) site must be willing and able (in the opinion of the
             treating physician) to undergo two research biopsies for the investigational component
             of this trial.

          -  A subset of participants (6 participants per treatment arm) treated at the lead UW
             site must be willing to undergo NaF PET/CT scans for the investigational component of
             this trial.

          -  For those participants who are sexually active, they must be willing to use barrier
             contraceptive methods, and refrain from donating sperm, during the period of treatment
             on this trial and for four weeks after the last DNA immunization treatment

          -  Participants must be informed of the experimental nature of the study and its
             potential risks, and must sign an Institutional Review Board (IRB)-approved written
             informed consent form indicating such an understanding

        Exclusion Criteria:

          -  Small cell or other variant (non-adenocarcinoma) prostate cancer histology, unless
             there is evidence that the tumor expresses PAP

          -  Participants may not be receiving other investigational agents or be receiving
             concurrent anticancer therapy other than standard androgen deprivation therapy

          -  Concurrent bisphosphonate therapy is not excluded, however participants should not
             start bisphosphonate therapy while on this study; those participants already receiving
             bisphosphonate therapy should continue at the same dosing and schedule as prior to
             study entry

          -  Rapidly progressive symptomatic metastatic disease, as defined by the need for
             increased opioid analgesics within one month of registration for the treatment of pain
             attributed to a prostate cancer metastatic lesion; participants receiving opioids must
             receive approval from the PI for eligibility

          -  5. Treatment with any of the following medications within 28 days of day 1, or while
             on study, is prohibited:

               -  Systemic corticosteroids (at doses over the equivalent of 5 mg prednisone daily);
                  inhaled, intranasal or topical corticosteroids are acceptable

               -  Prostate Cancer and spes (PC-SPES)

               -  Megestrol

               -  Ketoconazole

               -  5-α-reductase inhibitors - participants already taking 5-α-reductase inhibitors
                  prior to 28 days prior to registration may stay on these agents throughout the
                  course of therapy, but these should not be started while participants are on
                  study

               -  Diethyl stilbesterol

               -  Abiraterone

               -  Enzalutamide

               -  Apalutamide

               -  Radium 223 (Xofigo®)

               -  Any other hormonal agent or supplement being used with the intent of cancer
                  treatment must be reviewed by the PI for eligibility

          -  External beam radiation therapy within 4 weeks of registration is prohibited, or
             anticipated need for radiation therapy (e.g. imminent pathological fracture or spinal
             cord compression) within 3 months of registration. Participants must have recovered
             from all radiation-related toxicities and not have had radiation pneumonitis.

          -  Major surgery within 4 weeks of registration is prohibited

          -  Prior cytotoxic chemotherapy (for example, but not limited to, docetaxel,
             mitoxantrone, cabazitaxel) within 3 months of registration is prohibited

          -  Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, or with any agent
             directed to another T-cell stimulatory or inhibitory receptor (e.g. CTLA-4, OX-40,
             CD137).

          -  Participants with a history of life-threatening autoimmune disease

          -  Participants with a history of non-infectious pneumonitis that required corticosteroid
             treatment, or has current pneumonitis

          -  Participants with a history of allergic reactions to the tetanus vaccine

          -  Participants who have undergone splenectomy or who have a diagnosis of
             immunodeficiency

          -  Participants must not have other active malignancies other than non-melanoma skin
             cancers or superficial (non-muscle-invasive) carcinoma of the bladder. Participants
             with a history of other cancers who have been adequately treated and have been
             recurrence-free for > 3 years are eligible.

          -  Participants with known brain metastases and/or carcinomatous meningitis

          -  Participants who have received a live vaccine within 30 days prior to the first dose
             of study drug. Examples of live vaccines include, but are not limited to, the
             following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever,
             rabies, Bacillus Calmette - Guérin (BCG), and typhoid vaccine. Seasonal influenza
             vaccines for injection are generally killed virus vaccines and are allowed; however,
             intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not
             allowed.

          -  Any antibiotic therapy within 1 month of day 1, or anticipated need for antibiotic
             therapy within 1 month of beginning treatment

          -  Participants with 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 (eg., thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is
             not considered a form of systemic treatment.

          -  Any other medical intervention or condition, which, in the opinion of the PI or
             treating physician, could compromise participant safety or adherence with the study
             requirements (including biopsies), or confound results of the study, over the
             treatment period.

          -  Any known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirement of the trial.

          -  Participants cannot have concurrent enrollment on other phase I, II, or III
             investigational treatment studies.