Multiple myeloma (MM) patients mount suboptimal neutralizing antibodies (nAb) following 2-doses of SARS-CoV-2 mRNA vaccines. Currently circulating SARS-CoV-2 variants of concern (VOC) carry the risk of breakthrough infections. We evaluated immune recognition of current VOC including BA.1, BA.2 and BA.5 in 331 racially representative MM patients following 2 or 3 doses of mRNA vaccines. Third dose increased nAbs against WA1 in 82% but against BA variants in only 33-44% of patients. Vaccine-induced nAbs correlated with RBD-specific class-switched memory B cells. Vaccine-induced spike-specific T-cells were detected in patients without seroconversion and cross-recognized variant-specific peptides but were predominantly CD4+ T-cells. Detailed clinical/immunophenotypic analysis identified features correlating with nAb/B/T cell responses. Patients who developed breakthrough infections following 3 vaccine doses had lower live-virus nAbs, including against VOC. MM patients remain susceptible to SARS-CoV-2 variants following 3 vaccine doses and should be prioritized for emerging approaches to elicit variant-nAb and CD8+ T-cells.