• Patients receiving concomitant immunosuppressive agents for medical condition. • Patients who need definitive radiotherapy for treatment of reMB/PNET. Focal boost radiotherapy may be delivered prior to immunotherapy if required for local control. • Patients receiving any other concurrent anticancer or investigational drug therapy. • Patients with any clinically significant unr elated systemic illness (serious infections or significant cardiac, pulmonary, hepatic or other organ dysfunction). • Patients with inability to return for follow -up visits or obtain follow -up studies required to assess toxicity to therapy. Study Design: This prospective Phase II multi -institutional clinical trial will evaluate the progression -free survival of autologous tumor -specific T cell immunotherapy (TTRNA -xALT) in conjunction with TTRNA- loaded dendritic cell vaccine in patients with first recurrenc e of medulloblastoma (reMB)/supratentorial primitive neuroectodermal tumors (PNETs) after completion of definitive radiation therapy . Up to 42 patients will be enrolled to treat 35 evaluable patients with reMB/PNET with DC + xALT therapy. Following surg ical resection, biopsy, or cytology examination with confirmatory pathologic diagnosis, patients will be enrolled into HDC (Group A) or NMA salvage chemotherapy (Group B) based on eligibility for HDC. Patients with localized relapse and have not failed HD C+PBSCT previously will be enrolled into Group A as HDC+PBSCT is considered an acceptable standard -of-care in the relapsed disease setting. Patients with disseminated disease, have previously failed HDC+PBSCT, or are otherwise considered poor candidates for HDC based on overall health status, but otherwise meet eligibility criteria, will be enrolled into Group B and will receive a salvage chemotherapy regimen followed by non- myeloablative cyclophosphamide/fludarabine lymphodepletive conditioning and PBSCT prior to DC + xALT therapy. For purposes of this protocol, localized relapse will be defined as recurrence in the same CNS location as the original tumor or a single location outside of the primary site. Disseminated disease will be defined as new lesions with little evidence of being contiguous with prior resection cavity, or intraventricular spread, or dissemination along any anatomically definable subcortical white matter tracts. Group A : Patients enrolled into Group A will receive Induction chemothera py that will include cyclophosphamide, etoposide, and temozolomide. Leukapheresis for collection of autologous peripheral blood stem cells (PBSCs) and peripheral blood mononuclear cells (PBMCs) for DC and T cell generation will occur prior to and during i nduction cycles of chemotherapy and will continue until adequate quantities of nucleated cells are obtained. The leukapheresis products will be aliquoted for future autologous PBSC rescue during Consolidation and used to generate the TTRNA -xALT and multiple doses of the TTRNA -DCs for future use during Post -transplant Immunotherapy. After completion of Induction, eligible patients will proceed to Consolidation with high dose chemotherapy consisting of carboplatin, etoposide, and thiotepa, followed by autologous PBSC rescue. The following day, Post -transplant Immunotherapy begins with infusion of the TTRNA -xALT and injection of the first TTRNA -DC vaccine embedded with GM -CSF 150 ug followed by G -CSF (5 micrograms/kg/day beginning no later than day 6 until c ount recovery). Patients will receive TTRNA -xALT at 3x107 cells/kg at vaccine #1 in combination with the first Re-MATC H Protocol Page 25 of 106 Version: 20180628 of three biweekly fixed doses of TTRNA -DC (1x107 cells) with GM -CSF. Vaccines #2 and #3 will consist of intradermal DC with GM -CSF vaccination only. Enrolled patients with reMB/PNETs will receive 3 -4 cycles of induction therapy consisting of two four week cycles of intravenous cyclophosphamide (2 gm/m2/day for 2 days as Cycles 1 and 2) followed by two four week cycles of oral etoposide 30 mg/m2/day for 14 days plus oral temozolomide (TMZ) (150 mg/m2/d for 5 days as Cycles 3 and 4). Patients will undergo a non- mobilized leukapheresis prior to induction chemotherapy for harvest of peripheral blood mononuclear cells (PBMCs) for TTRNA -xALT and TTRN A-DC generation. Afterwards, mobilized peripheral blood stem cells (PBSC) will be collected after each induction chemotherapy cycle until enough peripheral blood stem cells (PBSCs) are harvested for autologous stem cell rescue (minimum of 2x10 6 CD34+ PBSCs /kg) Patients who have radiographic or histologic evidence of progression will be replaced. If either DCs and/ or xALT do not meet release criteria or targeted dose then the patient may remain on study and receive the qualified product but will be replaced for the purposes of safety and efficacy assessment. For the purpose of this study, progression will be defined as a new lesion confirmed by biopsy or resection, positive cerebrospinal fluid (CSF) cytology, or radiographic progression as defined by protocol criteria . Following recovery from the 3rd or 4th cycle of induction chemotherapy (ANC > 1000 cells/ µL), patients will undergo disease restaging and organ function evaluation. Patients will be admitted to the Pediatric Bone Marrow Transplant Unit (BMTU) and receive Carboplatin (either 500 mg/m 2 or a dose calculated based on Calvert’s formula and a AUC (Area under the concentration time curve) 7 mg/ml/min, whichever is less) on days - 8, -7, and - 6, followed by thiotepa 300 mg/m 2 and etoposide 250 mg /m2 daily on days - 5, -4, and - 3. Three days after HDC (Day 0), patients will receive PBSC rescue. DC + xALT therapy will begin 24 hours after PBSCT. These patients will receive TTRNA -xALT (3x10 7/kg i.v.) and TTRNA -DCs (1x107 cells i.d.) following the transplant as vaccine #1. Patients will receive 3 biweekly TTRNA -DC vaccines with GM -CSF as long as clinically stable. Patients will also receive G-CSF 5 microgram/kg/day beginning no later than day 6 until ANC recovers to >1000 cells/ µL. NOTE: Patient s who are no longer candidates for HDC will be eligible to transfer from Group A to Group B. Group B: Patients enrolled into Group B will receive NMA salvage chemotherapy that will include cycles of etoposide, and temozolomide followed by cyclophosphamide and fludarabine. Enrolled patients with reMB/PNETs will receive salvage chemotherapy consisting of 2 -4 cycles of oral etoposide 30 mg/m2/day for 14 days plus oral temozolomide (TMZ) 150 mg/m2/d for 5 days monthly until Immunotherapy prepa ration is complete. Patients will undergo a non -mobilized leukapheresis prior to salvage chemotherapy for harvest of peripheral blood mononuclear cells (PBMCs) for TTRNA -xALT and TTRNA -DC generation. Afterwards, mobilized leukapheresis will be attempted a fter each salvage chemotherapy cycle until enough peripheral blood stem cells (PBSCs) are harvested for autologous stem cell infusion (goal of 2x10 6 CD34+ PBSCs/kg ). Subjects who do not mobilize any peripheral blood stem cells or do not undergo leukaphere sis, will continue with immunotherapy without NMAchemotherapy. If either DCs and/or xALT do not meet release criteria or targeted dose, then the patient may remain on study and receive the qualified product but will be replaced for the purposes of safety assessment. Patients who progress prior to receiving immunotherapy may remain on study as long as they continue to meet the other eligibility criteria. Patients may receive the first 3 vaccines as long as they are clinically stable Re-MATC H Protocol Page 26 of 106 Version: 20180628 and remain eligible. S ubsequently, for the purpose of this study, progression will be a new lesion confirmed by biopsy or resection, positive cerebrospinal fluid (CSF) cytology (when previously negative), or radiographic progression as defined by protocol criteria. Following s urgery and leukapheresis, adequate organ function testing will be repeated prior to initiation of cyclophosphamide and fludarabine conditioning. Drug administration and dosage for the lymphodepletive conditioning may be adjusted based upon hematologic per formance and organ function testing results as per protocol. After completion of NMA salvage chemotherapy and starting 11 days before Immunotherapy, patients will receive 2 days of cyclophosphamide I.V. at 1g/m 2, followed by 5 days of fludarabine I.V. at 25 mg/m2. Approximately 72 hours following fludarabine, PBSCs , if available, will be infused. Approximately 96 hours following the final dose of fludarabine, Immunotherapy begins with infusion of TTRNA -xALT and injection of the first TTRNA -DC vaccine. Patients will receive G -CSF after DC + xALT therapy until ANC recovers to >1000 cells/ µL. Patients will receive TTRNA -xALT at 3x107 cells/kg with the 3 total biweekly fixed doses of TTRNA -DC (1x107 cells i.d.) with GM -CSF 150 ug . The NMA recovery will incorporate G -CSF at 5 microgram/kg/day beginning no later than day 6 until ANC recovers to >1000 cells/ µL. NOTE: Patients on Group B with ANC <1000/µL and/or platelet count <100,000/µL prior to NMA will be allowed to get vaccine and ALT infusion; however, NMA conditioning will be withheld . Based on prior chemotherapy history and/or hematologic performance, patients enrolled on Group B receiving salvage chemotherapy may need to have adjustment to the planned chemotherapy regimen a t the discretion of the treating physician(s). Focal boost radiotherapy may be delivered prior to immunotherapy if required for local control. As no salvage chemotherapy regimens in the recurrent setting of MB or PNETs have been found to be curative or achieve significantly prolonged disease -free survival, we do not anticipate any clinical impact of adjustments to the planned regimen in assessing PFS endpoint. All chemotherapy regimens will be recorded and any deviation from the prescribed regimen above noted. The primary efficacy endpoint will be 12- month progression- free survival (PFS -12) rate after treatment with DC + xALT therapy as a surrogate for overall survival. Gururangan et al. reported that PFS -12 for patients with recurrent disease after in itiating treatment with HDC + PBSCT or standard salvage therapy was 33% (95% confidence interval of 10%, 59%) and two -year PFS of 0%. The population of patients that will be treated in the current protocol in Group A is similar to the subset of patients t reated on the Gururangan regimen. Due to the complexity and expense of adoptive cellular therapy treatment, if the true PFS -12 associated with DC + xALT therapy is 33%, there would be limited interest in further investigation of this treatment regimen without significant modification to improve efficacy. However, if the true PFS -12 were 55% or greater, there would be interest in studying this treatment regimen within the context of larger confirmatory Phase II or III clinical trials. Within Group B, a go od historical benchmark for this patient population receiving a standardized salvage regimen is not readily available. However, previously published studies have shown that patients unable to receive HDC and receive salvage regimens for recurrent disease generally have poorer prognosis than patients in Group A with localized disease relapse receiving HDC + PBSCT. These differences, however, did not result in a statistically significant difference in survival outcomes between patients receiving HDC+PBSCT vs salvage chemotherapy. Therefore, we will conservatively use the benchmark described above for analysis Re-MATC H Protocol Page 27 of 106 Version: 20180628 of all patients collectively for the primary 12 -month PFS endpoint. With that assumption, the overall sample size justification described above is for evaluable patients on both treatment arms. Therefore, the study is designed to differentiate between a PFS -12 rate of 33% (null hypothesis) and 55% (alternative hypothesis). With a total of 35 patients enrolled in the Phase II trial, this assessment ha s 90% power assuming a type I error rate of 0.10. There is also 97% power to differentiate between PFS -12 rates of 33% and 60%. PFS and OS for patients enrolled on Group A and Group B will also be analyzed separately as a descriptive analysis to explore the possibility that treatment outcomes may differ significantly on the two treatment arms in this study. Immune Monitoring: Peripheral blood will be drawn prior to non- mobilized leukapheresis , prior to immunotherapy , 1 day post Vaccine #1, 4 (+/- 1) days post Vaccine #1, weekly post V accine #1 for six weeks , and bimonthly , if feasible, until progression for T cell kinetics. Blood will be processed in accordance with SOP-UFBTIP -126. DCs will be given intradermally and divided equally to both inguinal regions. Vaccines #2 and #3 will occur at 2 week intervals following the first dose. Patients will be followed bi -monthly (+/- one month) for the first year post -immunotherapy, then every 3 months (+ /- one month) until tumor progression and death due to any cause. As part of standard care for these patients, upon tumor progression, participants may undergo stereotactic biopsy or resection. As this is not a research procedure, consent will be obtained separately. If tissue is obtained, it will be used to confirm tumor progression histologically and to assess immunologic cell infiltration and antigen expression profile in recurrent lesions. Re-MATC H Protocol Page 28 of 106 Version: 20180628 2.2 Multi -Site Study Schema Re-MATC H Protocol Page 29 of 106 Version: 20180628 2.3 Study Schema for Group A Re-MATC H Protocol Page 30 of 106 Version: 20180628 2.4 Study Schema for Group B Re-MATC H Protocol Page 31 of 106 Version: 20180628 3. PRINCIPAL INVESTIGAT OR (PI) AND STUDY STAFF DUANE A.