Inclusion Criteria:

          1. Eastern Cooperative Oncology Group (ECOG) performance status of <=2.

          2. Has received previous myeloma-specific therapy.

          3. In the Combination Cohort (TAK-079-PomDex) only must be able to take concurrent
             prophylactic anticoagulation per standard clinical practice as directed by the
             investigator and the Pomalyst product information.

          4. Documentation of RRMM as defined by the International Myeloma Working Group (IMWG)
             criteria.

          5. For Participants with MM, measurable disease defined as one of the following:

               -  Serum M-protein >=0.5 g/dL (>=5 gram per liter [g/L]).

               -  Urine M-protein >=200 mg/24 hours.

               -  In participants without measurable M-protein in serum protein electrophoresis
                  (SPEP) or urine protein electrophoresis (UPEP), a serum FLC assay result with
                  involved FLC level >=10 mg/dL (>=100 milligram per liter [mg/L]), provided serum
                  FLC ratio is abnormal.

          6. Prior therapy should meet all the following criteria:

             Participants in the dose Escalation Cohort (escalation phase) and participants in the
             dose Confirmation Cohort;

               -  Should be previously treated with at least a proteasome inhibitor (PI), an
                  immunomodulatory drug (IMiD), and a steroid. Note: Participants who have had a
                  previous autologous stem cell transplant will have additionally been exposed to
                  an alkylating agent; however, participant who have not had a previous autologous
                  stem cell transplant may not have been exposed to an alkylating agent per
                  standard practice.

               -  Should be refractory or intolerant to at least 1 PI and at least 1 IMiD.

               -  Should either have received >= 3 prior lines of therapy or should have received
                  at least 2 prior lines of therapy if one of those lines included a combination of
                  PI and IMiD.

               -  In phase 1, previous exposure to an anti-CD38 agent, as a single agent or in
                  combination, is allowed but is not required. (Participants in the dose Escalation
                  Cohort).

               -  In phase 1 dose Confirmation Cohort, cohorts of participants that are refractory
                  at any time to at least 1 anti-CD38 agent or who are anti-CD38 naïve will be
                  enrolled.

             Participants in the Combination Cohort (TAK-079 added to PomDex cohort only):

               -  Have undergone prior therapy with >=2 prior anti-myeloma therapies (line of
                  therapy defined below).

               -  Has either relapsed or relapsed and refractory disease. Should have progressed on
                  or within 60 days of completing the last anti-myeloma therapy (refractory defined
                  below).

          7. In the phase 2a portion of the study, up to 2 cohorts of participants with RRMM may be
             enrolled: 1 that is refractory to at least 1 anti-CD38 monoclonal antibody (mAb)
             therapy at any time during treatment and 1 that is naïve to daratumumab.

        Note:

        o Refractory is defined as at least a 25% increase in M-protein (response of stable disease
        during prior therapy) or PD during treatment or within 60 days after last dose of prior
        therapy.

        Exclusion Criteria:

          1. Sensory or motor neuropathy of National Cancer Institute Common Terminology Criteria
             for Adverse Events (NCI CTCAE) Grade >=3.

          2. Have received allogeneic stem cell transplant.

          3. Have received anti-CD38 antibody therapy and do not fulfill a 180-day washout period
             before receiving TAK-079.

          4. Not recovered from adverse reactions to prior myeloma treatment or procedures
             (chemotherapy, immunotherapy, radiation therapy) to NCI CTCAE Grade <=1 or baseline,
             excluding alopecia.

          5. Clinical signs of central nervous system (CNS) involvement of MM.

          6. Active chronic hepatitis B virus (HBV) or hepatitis C virus (HCV) infection, active
             HIV, or cytomegalovirus (CMV) infection.

          7. POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy and skin
             changes) syndrome, monoclonal gammopathy of unknown significance, smoldering myeloma,
             solitary plasmacytoma, amyloidosis, Waldenström macroglobulinemia, or IgM myeloma.

          8. Positive Coombs tests at screening.

          9. For participants in the Combination Cohort (TAK-079-PomDex) only: participant has
             previously received pomalidomide or has hypersensitivity to thalidomide or
             lenalidomide.