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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, TGF imprinted (TGFi), 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 + TGFi 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
* TGFi NK cells: via IV on Day 12

This ComboMATCH patient screening trial is the gateway to a coordinated set of clinical trials to study cancer treatment directed by genetic testing. Patients with solid tumors that have spread to nearby tissue or lymph nodes (locally advanced) or have spread to other places in the body (advanced) and have progressed on at least one line of standard systemic therapy or have no standard treatment that has been shown to prolong overall survival may be candidates for these trials. Genetic tests look at the unique genetic material (genes) of patients' tumor cells. Patients with some genetic changes or abnormalities (mutations) may benefit from treatment that targets that particular genetic mutation. ComboMATCH is designed to match patients to a treatment that may work to control their tumor and may help doctors plan better treatment for patients with locally advanced or advanced solid tumors.

The trial will use neoadjuvant hypofractionated radiotherapy followed by surgical resection in the treatment for soft tissue sarcoma. It will allow patients to be treated over a shorter course (5 or 15 days of radiation) compared to the traditional 5 week regimen. It is proposed that this will be possible without increasing the risk of wound complication or local recurrence compared with a traditional 5 week course of pre-operative radiation.

The purpose of this expanded access protocol (EAP) is to provide controlled access to Afamitresgene autoleucel, suspension for intravenous infusion that does not meet the commercial release specification (NC afami-cel). This EAP will be conducted at authorized treatment centers where TECELRA is being administered and where the EAP is approved to be conducted. Patients who are prescribed TECELRA , sign the informed consent form, and meet all entry criteria will be eligible to participate in this protocol.