FGFR4 Chimeric Antigen Receptor (CAR) T Cells in Children and Young Adults With Recurrent or Refractory Rhabdomyosarcoma

Background: Rhabdomyosarcoma (RMS) is a cancer of soft tissues. It is the most common soft tissue sarcoma seen in children. RMS cancer cells have a protein called FGFR4 on their surface. Researchers want to try a new kind of treatment for RMS: They will collect a person s own T cells, a type of immune cell; then they will change the T cells so they are better able to target the FGFR4 protein and attack RMS tumor cells. The modified T cells are chimeric antigen receptor (CAR) T cells. The treatment in this study is called FGFR4-CAR T cells. Objective: To test FGFR4-CAR T cells in children and young adults with RMS. Eligibility: People aged 3 to 39 years with RMS. The RMS must have failed to respond or returned after at least 2 rounds of standard treatment. Design: Participants will be screened. They will have physical exam, imaging scans, blood tests, and tests of their heart. They may have a tissue sample taken from their tumor. They will undergo apheresis: Blood will be taken from the body through a catheter. The blood will pass through a machine that separates out the T cells, and the remaining blood will be returned to the body. The collected T cells will be taken to a lab to create FGFR4-CAR T cells. Once the FGFR4-CART cells are ready, participants can receive these T cells. For 4 days they will receive drugs to prepare their body for the FGFR4-CAR T cells. After this, the modified T cells will be infused into a vein. Participants will be then monitored closely to watch for any side effects from the CART cells and be followed to see what effect the CART cells have on their tumors. They will have follow-up visits for up to 5 years. Long-term follow-up will be another 10 years.

* INCLUSION CRITERIA * Histologically confirmed rhabdomyosarcoma by the NCI Department of Pathology. Note: Since FGFR4 expression is universal in rhabdomyosarcoma, confirmation of FGFR4 expression is not required. * Relapsed or refractory rhabdomyosarcoma after at least two (2) cancer treatment regimens i.e., participants should have relapsed or progressed after upfront therapy (that includes any systemic chemotherapy with or without local control) as well as at least one salvage therapy (which can be systemic therapy, radiation, or surgery). * No available alternative curative therapies per standard of care. * Participants must have measurable disease per RECIST 1.1 or non-measurable disease on imaging. * Age \>= 3 and \=15 kg. * Performance status: Karnofsky \>= 50% (\>= 16 years) or Lansky \>= 50% (\< 16 years). Note: Participants who are unable to walk because of paralysis, but who are upright in a wheelchair will be considered ambulatory for calculating the performance score. * Participants must be willing to accept blood transfusions. * Adequate organ and marrow function as defined below: * Organ: Bone Marrow Function\* * Laboratory Element: Absolute neutrophil count; Minimum Requirement \>= 500/mcL * Laboratory Element: Platelets; Minimum Requirement \>= 50,000/mcL \*Transfusion independent (defined as no transfusion in the prior 7 days) for participants without bone marrow involvement. Participants who have bone marrow involvement with tumor are exempt from the platelet requirement and will not be evaluable for hematological toxicities. Participants must not be refractory to transfusions. * Organ: Liver Function * Laboratory Element: Aspartate aminotransferase (AST); Minimum Requirement \