Inclusion Criteria (Escalation)  Must be at least 18 years of age. Must sign an informed consent form (ICF) prior to any Screening procedures. Must have fresh bone marrow samples collected at Screening. Eastern Cooperative Oncology Group (ECOG) performance status (PS) score 0, 1, or 2. Has acceptable laboratory test results during the Screening period A woman of reproductive potential must agree to use adequate contraception during the trial and for 12 months after the last GEN3014 administration. A woman of childbearing potential must have a negative serum beta-human chorionic gonadotropin (β-hCG) at Screening. A woman must agree not to donate eggs (ova, oocytes) for assisted reproduction during the trial and for 12 months after receiving the last dose of GEN3014.  A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control.  Specific for RRMM:  Must have documented multiple myeloma as defined by the criteria below and have evidence of disease progression on the most recent prior treatment regimen based on IMWG criteria:  • Prior documentation of monoclonal plasma cells in the bone marrow ≥10% or presence of a biopsy-proven plasmacytoma.  and  • Measurable disease at baseline as defined by any of the following:  IgG, IgA, IgD, or IgM myeloma: Serum M-protein level ≥0.5 g/dL (≥5 g/L) or urine M protein level ≥200 mg/24 hours; Or Light chain myeloma: Serum Ig free light chain (FLC) ≥10 mg/dL and abnormal serum Ig kappa lambda FLC ratio  Note: Subjects with RRMM must have exhausted standard therapies, at the investigator's discretion.  For anti-CD38 mAb-naive RRMM Cohort: Subject received at least 3 prior lines of therapy including a PI and an IMiD in any order, or is double refractory to a PI and an IMiD; or subject received ≥ 2 prior lines of therapy if 1 of those lines included a combination of PI and IMiD. Note: Subjects should not have received any anti-CD38 antibody. Anti-CD38 mAb naive RRMM subjects will be recruited from countries where anti-CD38 therapies are not available. For anti-CD38 mAb-treated RRMM Cohort: Subject has received at least 2 prior lines of therapy and must have discontinued daratumumab or isatuximab for at least 4 weeks prior to the first dose of GEN3014. Note: Subjects should not have received any other anti-CD38 antibody except daratumumab or isatuximab. Potassium level ≥3.0 mEq/L (≥3.0 mmol/L); or corrected serum calcium ≤14.0 mg/dL (≤3.5 mmol/L).  Exclusion Criteria  Prior treatment with an anti-CD38 antibody except daratumumab or isatuximab. Treatment with an anti-cancer agent, chemotherapy, radiation therapy, or major surgery within 2 weeks prior to the first dose of GEN3014. Treatment with an investigational drug within 4 weeks or 5 half-lives, whichever is shorter, prior to the first dose of GEN3014. Cumulative dose of corticosteroids more than the equivalent of ≥140 mg of prednisone within 2-week period before the first dose of GEN3014. Has clinically significant cardiac disease. Toxicities from previous anti-cancer therapies have not resolved to baseline levels or to Grade 1 or less except for alopecia and peripheral neuropathy. Primary central nervous system (CNS) tumor or known CNS involvement at Screening. Has known history/positive serology for hepatitis B Known medical history or ongoing hepatitis C infection that has not been cured. HIV positive at screening Currently receiving any other investigational agents. A woman who is pregnant or breast-feeding, or who is planning to become pregnant while enrolled in this trial or within 12 months after the last dose of GEN3014. A man who plans to father a child while enrolled in this trial or within 12 months after the last dose of GEN3014.