Key Inclusion Criteria:

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1

          -  Confirmed diagnosis of active Multiple Myeloma (MM) by International Myeloma Working
             Group (IMWG) diagnostic criteria

          -  Patients must have myeloma that is response-evaluable according to the 2016 IMWG
             response criteria.

          -  Phase 1 Dose Escalation: Patients with MM who have exhausted all therapeutic options
             that are expected to provide meaningful clinical benefit, either through disease
             relapse, treatment refractory disease or intolerance of the therapy and including
             either:

               1. Progression on or after at least 3 lines of therapy, or intolerance of therapy,
                  including a proteasome inhibitor, an Immunomodulatory agent (IMiD), and an
                  anti-CD38 antibody, OR

               2. Progression on or after an anti-CD38 antibody and have disease that is "double
                  refractory" to a proteasome inhibitor and an IMiD, or intolerance of therapy. The
                  anti-CD38 antibody may have been administered alone or in combination with
                  another agent such as a proteasome inhibitor. Refractory disease is defined as
                  lack of response or relapse within 60 days of last treatment.

               3. Phase 2: Patients must be triple-refractory, defined as being refractory to prior
                  treatment with at least 1 anti-CD38 antibody, a proteasome inhibitor, and an
                  IMiD.

          -  Adequate hematologic and hepatic function as defined in protocol

          -  Serum creatinine clearance by Cockcroft-Gault >30 mL/min

        Key Exclusion Criteria:

          -  Diagnosis of plasma cell leukemia, amyloid light-chain amyloidosis,Waldenström
             macroglobulinemia (lymphoplasmacytic lymphoma), or POEMS syndrome (polyneuropathy,
             organomegaly, endocrinopathy, monoclonal protein, and skin changes)

          -  Patients with known MM brain lesions or meningeal involvement

          -  History of neurodegenerative condition, central nervous system (CNS) movement
             disorder, or patients with a history of seizure within 12 months prior to study
             enrollment are excluded.

          -  Continuous systemic corticosteroid treatment with more than 10 mg of prednisone or
             anti-inflammatory equivalent within 72 hours of start of study drug

          -  Treatment with any systemic standard or investigational anti-myeloma therapy within 5
             half-lives or within 28 days before first administration of study drug, whichever is
             shorter.

          -  Prior treatment with any anti-BCMA antibody (including antibody drug conjugate or
             bispecific antibody) or BCMA-directed CAR T therapy

          -  Uncontrolled infection with human immunodeficiency virus (HIV), hepatitis B virus
             (HBV) or hepatitis C virus (HCV) infection; or other uncontrolled infection

          -  Has known allergy or hypersensitivity to components of REGN5458

          -  History of allogeneic stem cell transplantation at any time, or autologous stem cell
             transplantation within 12 weeks of the start of study treatment

          -  Known hypersensitivity to both allopurinol and rasburicase

          -  Pregnant or breastfeeding women

          -  Women of childbearing potential and men who are unwilling to practice highly effective
             contraception prior to the initial dose/start of the first treatment, during the
             study, and for at least 6 months after the last dose.

          -  Another malignancy in the past 5 years, with the exception of non-melanoma skin cancer
             that has undergone potentially curative therapy or in situ cervical carcinoma, or any
             other tumor that has been deemed to be effectively treated with definitive local
             control and with curative intent.

        Note: Other protocol defined inclusion / exclusion criteria apply