EWSR1 Immunotherapy in Ewing Sarcoma and DSRCT

This study is for people who have high-risk Ewing sarcoma (ES), or a related Ewing's family tumor, desmoplastic small round cell tumor (DSRCT). The purpose of this study is to see if a new EWSR1 immunotherapy (a lipid nanoparticle coated with EWSR1 mRNA) which is given as a shot is safe and whether it can help the body's immune system better recognize and fight cancer. This EWSR1 immunotherapy is designed to target a specific genetic change (EWSR1 fusion gene) that is found in cancer cells but not in normal, healthy cells. Because the EWSR1 gene is broken in cancer cells and the small protein it makes are only in the ES or DSRCT cancer cells, the goal of EWSR1 immunotherapy is to help the immune system identify and attack the cancer without harming normal cells. It is not yet approved by the Food and Drug Administration (FDA). EWSR1 immunotherapy will be given as a shot into the muscle of the arm, leg, or buttock. If participants also receive botensilimab (4 doses after each EWSR1 immunotherapy shot) and balstilimab (an infusion every 2 weeks), these are given intravenously (IV) by a needle in the arm over 30 minutes. Participants in this study will receive treatment for about 6 months or until their cancer gets worse. Participants will remain in the study for follow-up for an additional year, for a total time of about 1.5 years in the study.

Inclusion Criteria: * Participants must have histologically confirmed Ewing sarcoma (ES) or desmoplastic small round cell tumor (DSRCT) and confirmation of fusion gene rearrangement and breakpoint EWSR1-FLI1, EWSR1-ERG, EWSR1-WT1, who have completed standard of care vincristine + doxorubicin + cyclophosphamide alternating with ifosfamide + etoposide (VDC/IE) and have relapsed or had metastatic disease or are very high-risk disease (Bosma groups C, D, E, and/or very poor necrosis after VDC/IE) are eligible. All EWSR1 immunotherapy monotherapy participants are expected to have completed standard of care VDC/IE chemotherapy with local control and have had end of therapy follow-up for \> 3 months. * Participants must have demonstrated HLA (human leukocyte antigens) fit with an EWSR1 gene fusion peptide contained in the EWSR1 immunotherapy, as determined by HLA-binding analysis of peptides that span the EWSR1 fusion gene breakpoint and analysis of HLA fit to one of the constructs included in EWSR1 immunotherapy. * Participants may have no evidence of active disease, detectable disease (e.g., lung metastases \< 1 cm or bone metastases), or measurable disease by iRECIST (Immune Response Evaluation Criteria in Solid Tumors) criteria. The presence of RECIST measurable disease is not required for study entry. * At least 1 line of prior therapy (VDC/IE) is needed. * Age. The first 3 EWSR1 immunotherapy monotherapy and combination therapy participants will be adults ≥ 18 years old. After safety analysis of EWSR1 immunotherapy monotherapy in adults and Institutional Review Board (IRB) approval, adolescents (13-17 years old and 40kg or more are eligible for EWSR1 immunotherapy monotherapy. After safety analysis of EWSR1 immunotherapy monotherapy in adolescents and IRB approval, adolescents will be eligible for combination therapy and children ages 12 years old or younger will be eligible for EWSR1 immunotherapy monotherapy. Only after safety analysis of EWSR1 immunotherapy monotherapy will any group become eligible for combination therapy. * Participants must have adequate organ and marrow function as defined below: * absolute neutrophil count ≥ 1000/microliter (mcL) * platelets ≥ 100,000/mcL * hemoglobin ≥ 8 g/dL (transfusion allowed) * total bilirubin ≤ 1.5 x ULN (upper normal limits) * AST(aspartate aminotransferase) / ALT (alanine aminotransferase) ≤ 2.5 x ULN * creatinine ≤ 60 mL/min/1.73 m2 or ≤ 1.5 mg/mcL if \< 18 yrs * Participants on inhaled corticosteroids or maintenance doses of hydrocortisone are allowed (e.g., 20 mg in morning, 10 mg in evening in adult participants on chronic corticosteroids or history of adrenal insufficiency). * Participants with treated brain metastases are eligible after central nervous system (CNS)-directed therapy (surgery or radiotherapy). If on corticosteroids these participants should be weaned to hydrocortisone (20 mg am/10 mg pm if ≥ 40 kg or if \< 40 kg (20-39.9 kg) hydrocortisone 10 mg am/5 mg pm). * Participants with leptomeningeal disease are eligible. If on corticosteroids these participants should be weaned to hydrocortisone (20 mg am/10mg pm if ≥ 40 kg or if \< 40 kg hydrocortisone 10 mg am/5 mg pm). * Performance Karnofsky or Lansky Scale ≥ 60% * Participants with ES or DSRCT are eligible for planned radiotherapy before or during protocol therapy (e.g., to treat symptomatic lesions or bone metastases that are not "indicator lesions"). * A washout period of 2 weeks from chemotherapy and return of any chemotherapy related or radiation adverse events (AEs) to grade 1 or to baseline prior to cancer treatment except lymphopenia is required. * The effects of EWSR1 immunotherapy on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control and/or abstinence for at least 90 days after last dose of EWSR1 immunotherapy. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document; minors must assent. * Women of childbearing potential to have negative pregnancy test within 7 days of EWSR1 immunotherapy dosing. Exclusion Criteria: * Participants on concurrent chemotherapy or other immunotherapy. * Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities ≥ Grade 2) with the exception of alopecia and lymphopenia, post-nadir neutropenia and thrombocytopenia, and decreased function that has achieved a "new and stable baseline" from cancer, surgery, or radiation. * Participants who are receiving any other investigational agents. * Participants on total parenteral nutrition. * History of severe allergic reactions (anaphylaxis) attributed to compounds of similar chemical or biologic composition to EWSR1 immunotherapy. * Participants with uncontrolled infection (e.g., on intravenous antibiotics or with symptoms of fever attributable to infection). * Pregnant women are excluded from this study because of the unknown effects of EWS immunotherapy, botensilimab and balstilimab and their potential for teratogenic or abortifacient effects. * Participants who are unwilling or unable to comply with required study visits are ineligible. * Recent (\< 2 weeks) vaccine use, active HIV/Hep B/C, or any current or prior medical condition or therapy that, in the opinion of the treating investigator, could confound the results of the trial or is not in the best interest of the participant to participate. * Any participant with congestive heart failure (as defined by New York Heart Association Functional Classification III or IV), unstable angina, serious uncontrolled heart arrythmia, a myocardial infarction within 6 months prior to study entry, or a history of myocarditis. * Inadequate pulmonary function as defined by baseline pulse oximetry 92% or less on room air.