This phase I trial tests the effect of allogeneic Orca-Q stem cell transplant in treating patients with high-risk multiple myeloma that has come back after a period of improvement (relapsed) or that has not responded to previous treatment (refractory). An allogeneic (donor) transplant uses blood forming stem cells (graft) from a matched donor. When the healthy blood forming (stem) cells from a donor are infused into a patient, they may help the patient's bone marrow make more healthy cells and platelets and may help destroy any remaining cancer cells. Sometimes the transplanted cells from a donor can attack the body's normal cells (called graft-versus-host disease \[GVHD\]). Orca-Q includes some T cells (a type a white blood cell) that are thought to help prevent some of the known complications as well as help attack the cancer cells. However, Orca-Q removes a specific type of T cell called naive T lymphocytes. Naive T cells may contribute to GVHD and are not thought to be required for the success of the treatment. Removing these cells may help reduce the frequency or severity of GVHD. Giving chemotherapy, such as thiotepa, busulfan, and fludarabine, before a donor stem cell transplant helps kill cancer cells in the body and prepare the body to receive the transplant graft. Giving allogeneic Orca-Q may be safe, tolerable, and/or effective in treating patients with relapsed or refractory (R/R) high-risk multiple myeloma.