Key Inclusion Criteria:

          1. Diagnosis of multiple myeloma (MM) with relapsed and/or refractory (R/R) disease.
             Participants must have received at least 3 prior anti-myeloma treatment regimens.
             Participants must have previously received all of the following therapies and must be
             refractory to the last line of therapy prior to entering the study (not applicable to
             Phase 2a):

               1. Autologous stem cell transplant

               2. A regimen that included an immunomodulatory agent (eg, thalidomide, lenalidomide,
                  pomalidomide) and a proteasome inhibitor (eg, bortezomib, carfilzomib, ixazomib),
                  either alone or in combination

               3. Anti-CD38 (eg, daratumumab) as part of a combination regimen or as a monotherapy

             Subjects who have received prior allogeneic stem cell transplant or donor lymphocyte
             infusion at least 100 days before enrollment with no signs of acute or chronic
             graft-versus-host disease (GVHD) will be considered eligible. Subjects who were not
             candidates to receive one or more of the above treatments (ie, contraindicated) are
             eligible.

          2. Subjects must have measurable disease.

          3. Subject must be willing to provide fresh bone marrow biopsy samples during Screening
             (and prior to study treatment, if required).

          4. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

          5. Adequate renal, bone marrow, hepatic, pulmonary, and cardiac function

          6. Phase 2a cohorts only - Subjects with R/R MM who have been previously treated with
             prior BCMA-directed anti-myeloma therapy, achieved at least a partial response (PR)
             and progressed on the following treatment:

               1. Subjects who have received prior BCMA-directed CAR T-cell therapy. The last CAR
                  T-cell therapy must have been received at least 6 months prior to JCARH125
                  screening.

               2. Subjects who have received prior BCMA-directed T-cell engager therapy.

               3. Subjects who have received prior BCMA-directed antibody-drug conjugate therapy.

        Exclusion Criteria:

          1. Subjects with known active or history of CNS involvement by malignancy

          2. Subjects with solitary plasmacytoma; active or history of plasma cell leukemia (PCL);
             Waldenstrom's macroglobulinemia; Polyneuropathy, Organomegaly, Endocrinopathy,
             Monoclonal plasmaproliferative disorder, Skin changes (POEMS) syndrome; or symptomatic
             amyloidosis

          3. Subjects who are considered eligible to receive and have not refused an autologous
             stem cell transplant

          4. History of another primary malignancy that has not been in remission for at least 3
             years. The following are exempt from the 3-year limit: non-melanoma skin cancer,
             curatively treated localized prostate cancer, cervical carcinoma in situ on biopsy or
             a squamous intraepithelial lesion on Pap smear, and in situ breast cancer that has
             been completely resected.

          5. Require systemic immunosuppressive therapies (eg, calcineurin inhibitors,
             methotrexate, mycophenolate, rapamycin, thalidomide, immunosuppressive antibodies such
             as anti-IL-6 or anti-IL-6 receptor [IL-6R])

          6. Prior CAR T-cell or other genetically-modified T-cell therapy (not applicable for
             subjects enrolled in Phase 2a cohorts)

          7. Prior treatment with a BCMA-targeted agent (not applicable for subjects enrolled in
             Phase 2a cohorts)

          8. History or presence of clinically relevant CNS pathology such as epilepsy, seizure,
             paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease,
             cerebellar disease, organic brain syndrome, or psychosis

          9. Untreated or active infection at time of initial screening, at the time of
             leukapheresis, within 72 hrs before lymphodepletion, or 5 days before JCARH125
             infusion.

         10. History of any of the following cardiovascular conditions within 6 months of
             screening: Class III or IV heart failure as defined by the New York Heart Association
             (NYHA), myocardial infarction, unstable angina, uncontrolled or symptomatic atrial
             arrhythmias, any ventricular arrhythmias, or other clinically significant cardiac
             disease

         11. Subjects with known hypersensitivity to E Coli-derived proteins (only applicable to
             subjects in Phase 1 Anakinra Cohort)

         12. History of severe immediate hypersensitivity reaction to any of the protocol-mandated
             or recommended agents used in this study