A Multi-Institution Study of TGFβ Imprinted, Ex Vivo Expanded Universal Donor NK Cell Infusions as Adoptive Immunotherapy in Combination With Gemcitabine and Docetaxel in Patients With Relapsed or Refractory Pediatric Bone and Soft Tissue

The purpose of this study is to determine if the addition of infusions of a type of immune cell called a "natural killer", or NK cell to the sarcoma chemotherapy regimen GEM/DOX (gemcitabine and docetaxel) can improve outcomes in people with childhood sarcomas that have relapsed or not responded to prior therapies. The goals of this study are: * To determine the safety and efficacy of the addition of adoptive transfer of universal donor, TGFβ imprinted (TGFβi), expanded NK cells to the pediatric sarcoma salvage chemotherapeutic regimen gemcitabine/docetaxel (GEM/DOX) for treatment of relapsed and refractory pediatric sarcomas To determine the 6-month progression free survival achieved with this treatment in patients within cohorts of relapsed or refractory osteosarcoma, Ewing sarcoma, rhabdomyosarcoma and non-rhabdomyosarcoma soft tissue sarcoma. * To identify toxicities related to treatment with GEM/DOX + TGFβi expanded NK cells Participants will receive study drugs that include chemotherapy and NK cells in cycles; each cycle is 21 days long and you can receive up to 8 cycles. * Gemcitabine (GEM): via IV on Days 1 and 8 * Docetaxel (DOX): via IV on Day 8 * Prophylactic dexamethasone: Day 7-9 to prevent fluid retention and hypersensitivity reaction * Peg-filgrastim (PEG-GCSF) or biosimilar: Day 9 to help your white blood cell recover and allow more chemotherapy to be given * TGFβi NK cells: via IV on Day 12