Pembrolizumab for the Treatment of Relapsed or Refractory Multiple Myeloma After Anti-BCMA CAR-T Therapies

Inclusion Criteria: 1. Male/female participants who are 18 years of age or older on the day of signing informed consent with histologically confirmed diagnosis of multiple myeloma will be enrolled in this study. 2. Ability to understand a written informed consent document, and the willingness to sign it or a legally acceptable representative (if applicable). 3. Have an Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%). Evaluation of ECOG is to be performed within 7 days prior to the start of study treatment. 4. The effects of pembrolizumab on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception for the duration of study participation and 120 days after last administration of study treatment. * Female participants are eligible if not pregnant, not breastfeeding, and one of the following: * Not a woman of childbearing potential (WOCBP) OR * WOCBP who agrees to follow contraceptive guidance during treatment period and at least 120 days following last dose of study treatment. * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 120 days after last administration of study treatment. Men should also refrain from donating sperm during this period. 5. Participants must have either * progressive disease after prior anti-BCMA CAR-T therapy and have not started another systemic anti-cancer therapy following progression after anti-BCMA CAR-T therapy. Patients who received localized radiotherapy alone for symptomatic relief of progressive disease following anti-BCMA CAR-T will be allowed. * OR * b. stable disease as best hematologic response after at least 30 days post anti-BCMA CAR-T infusion. Progression after anti-BCMA CAR-T is defined by International Myeloma Working Group (IMWG) criteria: 1. Increase of \> 25% from lowest response value in any one or more of the following: * Serum M-component and/or (the absolute increase must be \> 0.5 g/dL). * Urine M-component and/or (the absolute increase must be \> 200 mg/24 h). * Only in patients without measurable serum and urine M-protein levels; the difference between involved and uninvolved free light chain (FLC) levels. The absolute increase must be \> 10 mg/dL. * Bone marrow plasma cell percentage: the absolute percentage must be \> 10%. 2. Definite development of new bone lesions or soft tissue plasmacytomas or definite increase in the size of existing bone lesions or soft tissue plasmacytomas and/or 3. Development of hypercalcemia (corrected serum calcium \> 11.5 mg/dL or 2.65 mmol/L) that can be attributed solely to the plasma cell proliferative disorder. 6. Time from date of anti-BCMA CAR-T infusion to date of first administration of pembrolizumab (study drug) must be ≥ 30 days. In order to be eligible for this study, participants must not be candidates for treatment regimens known to provide clinical benefit in MM as assessed by the treating physician and must have previously received or are intolerant to a proteasome inhibitor, an immunomodulatory agent, and an anti-CD38 antibody. 7. Diagnosis of symptomatic multiple myeloma defined as: clonal bone marrow plasma cells \> 10% or biopsy-proven bony or extramedullary plasmacytoma and any one or more of the following calcium elevation, renal insufficiency, anemia, and bone abnormalities (CRAB) features and myeloma-defining events. 1. Hypercalcemia: serum calcium \> 0.25 mmol/L (\> 1 mg/dL) higher than the upper limit of normal or \> 2.75 mmol/L (\> 11 mg/dL). 2. Renal insufficiency: creatinine clearance \< 40 mL per minute or serum creatinine \> 177 micromol/L (\> 2 mg/dL). 3. Anemia: hemoglobin value of \>20g/L below the lowest limit of normal, or a hemoglobin value \<100 g/L. 4. Bone lesions: one or more osteolytic lesions on skeletal radiography, computed tomography (CT), or positron emission tomography (PET)/CT. If bone marrow has \< 10% clonal plasma cells, more than one bone lesion is required to distinguish from solitary plasmacytoma with minimal marrow involvement. 5. Any one or more of the following biomarkers of malignancy: * 60% or greater clonal plasma cells on bone marrow examination. * Serum involved / uninvolved free light chain ratio of 100 or greater, provided the absolute level of the involved light chain is at least 100 mg/L. * More than one focal lesion on magnetic resonance imaging (MRI) that is at least 5mm or greater in size. 8. Active and measurable disease, defined by serum paraprotein (M-protein) \>= 0.5 g/dL, 24-hour urine Bence Jones protein of \>= 200 mg, or abnormal serum free light chain ratio with involved light chain of \>= 10 mg/dL (100 mg/L). 9. Have adequate organ function as defined below. Specimens must be collected within 10 days prior to the start of study treatment: 1. Absolute neutrophil count (ANC) \>= 500/microliter (uL) (within 10 days prior to the start of study treatment). 2. Platelets \>= 25 000/uL (within 10 days prior to the start of study treatment). 3. Hemoglobin \>= 8.0 g/dL (within 10 days prior to the start of study treatment). * Growth factor and/or transfusion support is permissible to stabilize participant prior to study treatment if needed. * No lower limit if cytopenia is related to bone marrow involvement. 4. Creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (CrCl) \>= 30 mL/min for participant with creatinine levels \> 1.5 x institutional ULN (within 10 days prior to the start of study treatment). * Glomerular filtration rate (GFR) can also be used in place of creatinine or CrCl. * Creatinine clearance (CrCl) should be calculated per institutional standard. 5. Total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 x ULN (within 10 days prior to the start of study treatment). 6. Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 2.5 x ULN (=\< 5 x ULN for participants with liver metastases) (within 10 days prior to the start of study treatment). Exclusion Criteria: 1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to study treatment initiation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. \* Note: in the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication. 2. Has received prior therapy with an anti-programmed cell death protein 1 (anti PD-1), anti-programmed death-ligand 1 (anti PD-L1), or anti programmed cell death 1 ligand 2 (anti PD-L2) agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), OX 40, Cluster of Differentiation 137 (CD137)). 3. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to study treatment initiation. 1. Note: Participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline. Participants with =\< grade 2 neuropathy may be eligible. 2. Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. 4. Has received anti-BCMA CAR-T infusion \< 30 days prior to study treatment initiation. 5. Has received subsequent systemic anti-cancer therapy following anti-BCMA CAR-T therapy. Participants who received localized radiotherapy alone for symptom control following anti-BCMA CAR-T therapy will be allowed to participate. 6. Has 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-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccines are generally Messenger RNA (mRNA)-based or viral vector vaccines (replication-incompetent) and are allowed. 7. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. \* Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent 8. Has a diagnosis of primary immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 9. Has an active history of a second malignancy requiring treatment, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. Participants with the following low-risk or non-invasive malignancies will be allowed: 1. Basal cell carcinoma of the skin. 2. Squamous cell carcinoma of the skin. 3. Carcinoma in-situ of the cervix. 4. Carcinoma in-situ of the breast. 5. Superficial bladder cancer. 6. Incidental histologic finding of prostate cancer (T1a or T1b using the Classification of Malignant Tumors (TNM) \[tumor, nodes, metastasis\] clinical staging system) or prostate cancer that is curative or considered very-low or low risk in which observation is reasonable. 7. Other in-situ cancers. \* Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, or other in-situ cancers. 10. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable, and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention 11. Has severe hypersensitivity (\>= grade 3) to pembrolizumab and/or any of its excipients. 12. 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 and is allowed. 13. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 14. Has an active infection requiring systemic therapy. Prophylactic antibiotics/antivirals are allowed. 15. Has a known history of human immunodeficiency virus (HIV) infection. 16. Has known active Hepatitis B virus infection (defined as Hepatitis B (HBV) deoxyribonucleic acid (DNA) detected or Hepatitis B surface antigen (HbsAg) positive) or known active Hepatitis C virus infection (defined as Hepatitis C (HCV) ribonucleic acid (RNA) qualitative detected). Subjects who have been vaccinated against hepatitis B (positive for hepatitis B surface antibody (HBsAB)) who are negative for other markers of prior hepatitis B infection (e.g., Hepatitis B core antibody (HBcAb) negative) are eligible. Subjects with past exposure or known history of hepatitis B infection (e.g., HBcAb positive) are eligible for the study provided that they are negative by assessment for HBV DNA and HbsAg. Subjects with a history of hepatitis C infection (defined as detectable HCV antibody) are eligible as long as they have a negative HCV viral load. 17. Has a known history of active Bacillus Tuberculosis (TB). 18. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject 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. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. 21. Has had a history of allogenic bone marrow/tissue/solid organ transplant. 22. Has unmeasurable disease by serum/urine testing (oligo-secretory or non-secretory multiple myeloma). 23. Has diagnosis of Waldenstrom's disease, light chain amyloidosis, or polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, skin changes (POEMS) disease. 24. ECOG performance status \>= 2.