Inclusion Criteria:

          1. Be willing and able to provide written informed consent/assent for the trial prior to
             the performance of any protocol-related procedures that are not part of normal care.

          2. Be ≥ 18 years of age at the time the informed consent is signed.

          3. Histologically or cytologically documented adenocarcinoma of the prostate. Patients
             without histologically confirmed adenocarcinoma may be eligible if both the treating
             physician and the study PI agree that the patient's history is unambigulously
             indicative of advanced adenocarcinoma.

          4. Receive care through a Veterans Affairs Hospital.

          5. Have metastatic castration resistant prostate cancer with castrate-level testosterone
             (<50 ng/dL).

             a. Participants must maintain a castrate-level testosterone during the study.

          6. Have disease progression defined by one or more of the following three criteria:

               1. PSA > 2.0 ng/mL at time of screening and rising PSA by at least 2 consecutive
                  measurements a minimum of 1-week apart.

               2. Soft tissue progression as defined by Response Evaluation Criteria in Solid
                  Tumors (RECIST) version 1.1.

               3. Bone disease progression as defined by the PCWG3.

          7. Have measurable disease based on RECIST v.1.1 modified as described by the PCWG3 or
             non-measurable disease with bone metastases.

             a. Participants with measurable disease must have at least one lesion that is ≥10 mm
             in longest diameter for a soft tissue lesion, or ≥15 mm in short axis for a lymph
             node.

          8. Have a metastatic lesion that can be safely biopsied and be willing to undergo the
             tumor biopsy. If the participant is on anticoagulation, it must be safe to hold the
             anticoagulation for the biopsy.

          9. Have had a PSA response to enzalutamide (defined as a PSA decline of 50% or more), but
             now showing signs of PSA and/or radiographic progression per PCWG3 and/or RECIST 1.1.
             (Patients must be continuously on enzalutamide prior to joining study. They may not
             have had progression on enzalutamide and then challenge with new therapy and then
             restarted on enzalutamide.)

         10. Participants must discontinue antiandrogen therapy (ie, bicalutamide, flutamide,
             nilutamide) at least 4-6 weeks prior to registration with no evidence of PSA decline
             after washout.

               1. Bicalutamide: Washout period at least 6 weeks

               2. Flutamide and nilutamide: Washout period at least 4 weeks

         11. Participants must discontinue therapies for mCRPC, with the exception of GnRH agent,
             for 5 half-lives or 28 days, whichever is shorter.

               1. Prior treatment with sipuleucel-T, radium-223, or abiraterone is allowed.

               2. Tissue biopsy may be performed during washout period.

         12. Have a performance status of 0 or 1 according to the Eastern Cooperative Oncology
             Group (ECOG) scale.

         13. Demonstrate adequate organ function on screening laboratory tests performed within 14
             days of treatment initiation and as evidenced by:

               1. Hemoglobin ≥ 9.0 g/dL or ≥ 5.6 mmol/L without transfusion or erythropoietin (EPO)
                  dependency (within ≤ 7 days of assessment)

               2. WBC > 2,000/mm3 without growth factor support (within ≤ 7 days days of
                  assessment)

               3. Absolute neutrophil count ≥ 1,500/mm3 without growth factor support or
                  transfusion (within < 28 days of assessment)

               4. Platelet count ≥ 100,000/mm3

               5. Serum creatinine < 1.5 x upper limit of normal (ULN) or measured or calculated
                  (calculated per institutional standard) creatinine clearance ≥ 60 mL/min for
                  participant with creatinine levels > 1.5 x institutional ULN. GFR can also be
                  used in place of creatinine or CrCl.

               6. Serum total bilirubin < 1.5 x ULN or ≤ 2.0 x ULN for participants with liver
                  metastases

                    -  Participants with Gilbert's syndrome must have ≤ 3 x ULN and no liver
                       lesions

               7. Aspartate transaminase (AST) (SGOT) and alanine transaminase (ALT) (SGPT) ≤ 2.5 x
                  ULN or ≤ 5.0 x ULN for participants with liver metastases.

               8. Albumin ≥ 2.5 mg/dL.

               9. International normalized ratio (INR) or prothrombin time (PT) ≤ 1.5 x ULN unless
                  participant is receiving anticoagulant therapy, as long as PT is within
                  therapeutic range of intended use of anticoagulants.

              10. Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN unless participant is
                  receiving anticoagulant therapy, as long as PTT is within therapeutic range of
                  intended use of anticoagulants.

         14. Male participants of reproductive potential must agree to use an adequate method of
             contraception, starting with the first dose of study intervention and through 120 days
             after the last dose of study therapy. Contraception is not required if the patient's
             partner is a woman who is post-menopausal. Subjects of reproductive potential must
             agree to avoid impregnating a partner by complying with one of the following:

             Practice abstinence from heterosexual activity; abstinence (relative to heterosexual
             activity) can be used as the sole method of contraception if it is consistently
             employed as the subject's preferred and usual lifestyle. Periodic abstinence (e.g.,
             calendar, ovulation, sympto-thermal, post-ovulation methods, etc.) and withdrawal are
             not acceptable methods of contraception.

             OR

             Have their partner use acceptable contraception during heterosexual activity.
             Acceptable methods of contraception are:

             Single method (one of the following is acceptable):

               -  Intrauterine device (IUD)

               -  Contraceptive rod implanted into the skin.

             Combination method (requires use of two of the following):

               -  Diaphragm with spermicide (cannot be used in conjunction with cervical
                  cap/spermicide)

               -  Cervical cap with spermicide (nulliparous women only)

               -  Contraceptive sponge (nulliparous women only)

               -  Male condom or female condom (cannot be used together)

               -  Hormonal contraceptive: oral contraceptive pill (estrogen/progestin pill or
                  progestin-only pill), contraceptive skin patch, vaginal contraceptive ring, or
                  subcutaneous contraceptive injection.

         15. Participants must be able and willing to comply with the study visit schedule and
             study procedures.

        Exclusion Criteria:

          1. 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. Superficial bladder cancer is
             also permitted provided it is monitored and treated locally.

          2. Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis. Participants with previously treated brain metastases may participate
             provided they are stable (without evidence of progression by imaging for at least 4
             weeks prior to the first dose of study intervention 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 study intervention. This exception
             does not include carcinomatous meningitis, which is excluded regardless of clinical
             stability.

          3. Uncontrolled disease-related bone pain or other symptoms that suggest the participant
             should imminently go onto chemotherapy.

          4. Those with tumors having known microsatellite instability will be excluded.
             Participants found to have microsatellite instability in their tumors after analysis
             of the on-study biopsy will not be eligible to serve as FMT donors, but will be
             permitted on the study.

          5. Prior taxane-based chemotherapy (in any setting- castration sensitive or resistant).

          6. Has had prior therapy with an anti-CTLA4, anti-PD-1 or anti-PD-L1 antibody.

          7. Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to the
             first dose of study treatment or who has not recovered (ie, ≤ Grade 1 or at baseline)
             from adverse events due to agents administered more than 4 weeks earlier.

          8. Has received prior radiotherapy within 2 weeks of start of study treatment.
             Participants must have recovered from all radiation-related toxicities, not require
             corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted
             for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease.

          9. Has had prior targeted small molecule therapy within 2 weeks prior to the first dose
             of study treatment or who has not recovered (ie, ≤ Grade 1 or at baseline) from
             adverse events due to a previously administered agent.

               1. Note: Participants with ≤ Grade 2 neuropathy are an exception to this criterion
                  and may qualify for the study.

               2. Note: If a participant received major surgery, he must have recovered adequately
                  from the toxicity and/or complications from the intervention prior to starting
                  therapy.

         10. 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.

         11. Has received broad-spectrum antibiotics within 3 months of first dose of
             pembrolizumab.

         12. Has a history of seizure, unless he had a mass in his brain that has been removed,
             such as a meningioma.

         13. Has a diagnosis of immunodeficiency or conditions that need systemic corticosteroid
             replacement therapy > 10 mg/day prednisone (or equivalent) or other immunosuppressive
             medications within 28 days prior to the first dose of study intervention. Inhaled
             steroids are permitted if necessary.

         14. Has any active known or suspected autoimmune disease. Participants with vitiligo, type
             I diabetes mellitus, controlled autoimmune hypothyroidism, psoriasis not requiring
             systemic treatment, or other conditions under control are permitted to enroll.
             Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement
             therapy < 10 mg of prednisone/day for adrenal or pituitary insufficiency, etc.) is not
             considered a form of systemic treatment.

         15. Has a known history of active TB (Bacillus Tuberculosis).

         16. Has a history of (non-infectious) pneumonitis that required steroids or current
             pneumonitis .

         17. Has an active infection requiring systemic therapy.

         18. Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the participant's
             participation for the full duration of the trial, or is not in the best interest of
             the participant to participate, in the opinion of the treating investigator.

         19. Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

         20. Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients
             Testing positive for any of the following infectious diseases (criteria 21-22).

         21. Evidence of the following infectious agents:

               1. Stool pathogens: Clostridium difficilie toxin B by PCR, Giardia antigen,
                  Cryptosporidium antigen, Acid-fast stan for Cyclospora or Isospora, Ova and
                  parasites, Helicobacterial pylori antigen positivity, Salmonella spp., Shigella
                  spp., Campylobacter spp., Shiga-toxin producing Escherichia coli, Methicillin
                  Resistant Staphylococcus aureus, Vancomycin Resistant Enterococcus spp.,
                  Carbapenem Resistant Enterobacteriaceae, ESBL producing E. coli, Aeromonas spp.,
                  Plesiomonas spp., Yersinia spp., Vibrio spp., Entamoeba histolytica, Rotavirus,
                  Adenovirus, Norovirus

               2. Blood pathogens: Positive for HIV, type 1 or 2; Hepatitis A IgM; Hepatitis B
                  antigen, anti-HBC (both IgG and IgM), and anti-HBs; Hepatitis C antigen; T.
                  pallidum antibody; FTA-ABS (if positive T. pallidum screen)

         22. Risk factors for contracting an illness:

               1. Ongoing high-risk behaviors (e.g. men who have sex with men, men who have sex for
                  money, men who use intravenous drugs)

               2. Tattoo or body piercing within 6 months

               3. Risk factors for Creutzfeldt-Jakob disease

               4. Travel within the past 6 months to areas of the world where diarrheal illnesses
                  are endemic or risk of traveler's diarrhea is high

         23. Known current communicable disease (e.g. upper respiratory infection).

         24. Gastrointestinal co-morbidities: history of inflammatory bowel disease, history of
             irritable bowel syndrome, idiopathic chronic constipation, or chronic diarrhea,
             history of gastrointestinal malignancy or known polyposis.

         25. Major immunosuppressive medications, e.g., calcineurin inhibitors, exogenous
             glucocorticoids, biologic agents, etc.

         26. Systemic antineoplastic agents other than enzalutamide and LHRH agonist or antagonist.

         27. Has received a live vaccine within 30 days of planned start of study intervention.
             Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines
             and are allowed; however intranasal influenza vaccines (eg, Flu-Mist®) are live
             attenuated vaccines, and are not allowed.