This is a Phase 1 study to evaluate the safety of CB-011 (the study treatment), an allogeneic chimeric antigen receptor (CAR-T) cell therapy that targets the B cell maturation antigen (BCMA), to determine the best dose of CB-011, and to assess the effectiveness of CB-011 in treating multiple myeloma that has come back (relapsed) or that is no longer responding to other treatment (refractory).

Inclusion Criteria:

1. Documented diagnosis of relapsed/refractory multiple myeloma (MM) with measurable disease (according to IMWG diagnostic criteria.)
2. Received at least 3 prior MM treatment lines of therapy which must include a proteasome inhibitor (PI), an immunomodulatory drug (IMiD), and an anti-CD38 monoclonal antibody as part of a prior line of therapy, either in monotherapy or in combination.
3. Eastern Cooperative Oncology Group performance status grade of 0 or 1.
4. Adequate hematologic, renal, hepatic, pulmonary, and cardiac function.

Exclusion Criteria:

1. Prior treatment with CAR-T cell therapy directed at any target.
2. Autologous stem cell transplant within the last 6 weeks before lymphodepletion.
3. Allogeneic stem cell transplant within 6 months before lymphodepletion.
4. Known active or prior history of CNS involvement.
5. Stroke or seizure within 6 months of signing ICF.
6. Seropositive for or history of human immunodeficiency virus.
7. Vaccinated with live, attenuated vaccine within 4 weeks prior to lymphodepletion.
8. Hepatitis B infection.
9. Hepatitis C infection.
10. Known life-threatening allergies, hypersensitivity, or intolerance to CB-011 or its excipients.