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This phase II trial test whether combination chemotherapy works to improve blood test results in patients with high-risk multiple myeloma. Chemotherapy drugs, such as carfilzomib, daratumumab, lenalidomide, and dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. This trial may help determine if patients who have a small amount of cancer left after the initial treatment, called minimal residual disease, will benefit from the drug combination.
This phase II clinical trial studies how well personalized natural killer (NK) cell therapy works after chemotherapy and umbilical cord blood transplant in treating patients with myelodysplastic syndrome, leukemia, lymphoma or multiple myeloma. This clinical trial will test cord blood (CB) selection for human leukocyte antigen (HLA)-C1/x recipients based on HLA-killer-cell immunoglobulin-like receptor (KIR) typing, and adoptive therapy with CB-derived NK cells for HLA-C2/C2 patients. Natural killer cells may kill tumor cells that remain in the body after chemotherapy treatment and lessen the risk of graft versus host disease after cord blood transplant.