Inclusion Criteria:

          -  Confirmed diagnosis of multiple myeloma as defined by the International Myeloma
             Working Group (IMWG) criteria.

          -  Previously treated with at least 1 prior line of multiple myeloma (MM) therapy, and
             must have documented disease progression during or after their most recent therapy.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.

          -  Must have at least 1 aspect of measurable disease, defined as one of the following;

               1. Urine M-protein excretion >=200 mg per 24-hour, or

               2. Serum M-protein concentration >=0.5 grams per deciliter (g/dL), or

               3. Serum free light chain (FLC) assay: involved FLC level >=10 mg per dL (>=100 mg
                  per liter) and an abnormal serum free light chain ratio (<0.26 or >1.65).

          -  All prior treatment-related toxicities (defined by National Cancer Institute Common
             Toxicity Criteria for Adverse Events [NCI-CTCAE] version 5.0) must be <=Grade 1 at the
             time of enrollment, except for alopecia.

          -  Adequate organ function

        Exclusion Criteria:

          -  Intolerant to daratumumab.

          -  Refractory to daratumumab or any other anti-CD38 therapy (defined as progressive
             disease during treatment with anti-CD38 therapy, or within 60 days of completing that
             treatment).

          -  Intolerant to bortezomib, or refractory to bortezomib (defined as progressive disease
             during treatment with a bortezomib-containing regimen of 1.3 mg/m^2 twice weekly, or
             within 60 days of completing that treatment). Note: participants with progressive
             disease during treatment with a weekly bortezomib regimen are allowed.

          -  Ongoing Grade 2 or higher peripheral neuropathy or neuropathic pain.

          -  Prior treatment with anti-B-cell maturation antigen (anti-BCMA) therapy.

          -  Prior allogenic stem cell transplant.

          -  Any serious and/or unstable pre-existing medical, psychiatric disorder or other
             conditions, including renal, liver, cardiovascular, or certain prior malignancies.

          -  Corneal epithelial disease.