Inclusion Criteria:  Documented multiple myeloma as defined by the criteria: a. multiple myeloma diagnosis according to the International Myeloma Working Group (IMWG) diagnostic criteria, b. measurable disease at screening as defined by any of the following: 1) serum M-protein level greater than or equal to (>=) 0.5 gram per deciliter (g/dL); or 2) urine M-protein level >=200 milligrams (mg)/24 hours; or 3) serum immunoglobulin free light chain >=10 mg/dL and abnormal serum immunoglobulin kappa lambda free light chain ratio Received 1 to 3 prior line(s) of antimyeloma therapy including a proteasome inhibitor (PI) and lenalidomide; a. participants who have received only 1 line of prior line of antimyeloma therapy must be lenalidomide refractory. Progression on or within 60 days of the last dose of lenalidomide given as maintenance will meet this criterion Documented evidence of progressive disease based on investigator's determination of response by IMWG criteria on or after their last regimen Have an eastern cooperative oncology group (ECOG) performance status score of 0, 1, or 2 at screening and immediately prior to the start of administration of study treatment Have clinical laboratory values within the specified range  Exclusion Criteria:  Contraindications or life-threatening allergies, hypersensitivity, or intolerance to any study drug or its excipients. Additional exclusion criteria pertaining to specific study drugs include:  A participant is not eligible to receive daratumumab subcutaneous (SC) in combination with pomalidomide and dexamethasone (DPd) as control therapy if any of the following are present: 1) Contraindications or life-threatening allergies, hypersensitivity, or intolerance to pomalidomide, 2) Disease that is considered refractory to pomalidomide per IMWG, A participant is not eligible to receive daratumumab SC in combination with bortezomib and dexamethasone (DVd) as control therapy if any of the following are present: 1) Contraindications or life-threatening allergies, hypersensitivity, or intolerance to bortezomib, 2) Grade 1 peripheral neuropathy with pain or Grade >= 2 peripheral neuropathy as defined by National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) Version 5.0, 3) Disease that is considered refractory to bortezomib per IMWG, 4) Received a strong cytochromes P450 (CYP3A4) inducer within 5 half-lives prior to randomization Received any prior B cell maturation antigen (BCMA)-directed therapy Has disease that is considered refractory to an anti-cluster of differentiation 38 (CD38) monoclonal antibody per IMWG Received a cumulative dose of corticosteroids equivalent to >=140 mg of prednisone within 14 days before randomization Received a live, attenuated vaccine within 4 weeks before randomization Plasma cell leukemia at the time of screening, Waldenström's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, M-protein, and skin changes), or primary amyloid light chain amyloidosis