T cell-based therapies have shown remarkable efficacy in multiple myeloma (MM), yet the disease remains largely incurable. Here, we investigated the constant domains of the immunoglobulin heavy chain (IgH) as novel targets for therapeutic T cell receptors (TCRs), after confirming high and homogeneous IGH expression in >95% of MM patients. MM cells secrete excessive monoclonal immunoglobulins (M-proteins) that drive complications but are inaccessible to CAR T-cell or antibody targeting. Peptides from IgA and IgG constant regions were eluted from HLA-A*02:01, and reactive TCRs were isolated from healthy donors using allo-HLA-A*02:01 presentation to circumvent self-tolerance. T cells engineered with two TCRs specific for IgA or IgG passed a stringent multi-tier safety screen and selectively eliminated MM cells from 20 HLA-A*02:01+ patients secreting the relevant IgH in vitro. In vivo, IgA-TCR T cells eradicated IgA+HLA-A*02:01+ MM cells in xenograft models and reduced circulating IgA in humanized mice. These findings establish immunoglobulin constant domains as viable TCR targets in MM, potentially making ~40% of patients of European descent eligible for TCR T cell therapy, and extension to additional HLA alleles could further broaden eligibility. The approach may also be applicable to lymphoma and antibody-mediated autoimmune diseases.