9. STUDY POPULATION The target population for this study is children and young adults (age 0 -30 years) with recurrent MB, pineoblastoma, and cerebral P NETs who suffer first disease recurrence following standard radiotherapy +/ - craniospinal irradiation and who are candidates for HDC plus autologous stem cell rescue or NMA salvage chemotherapy . Patients with disease recurrence prior to completion of stand ard radiotherapy +/ - craniospinal irradiation will remain eligible as long as are first recurrence since completion of radiotherapy. Patients who are Re-MATC H Protocol Page 47 of 106 Version: 20180628 unable to receive radiotherapy due to genetic syndromes that put them at significant risk for secondary malignancies (i.e. Gorlin’s syndrome or NF1 mutation) are eligible at first recurrence/progression as these patients have failed definitive treatment. 10. INCLUSION CRI TERA 10.1 Inclusion Criteria Age: The patient must be ≤ 30 years of age at the time of enrollment. Disease Status : The patient must have a histologic ally confirmed first recurrence/progression of re MB/PNET (as confirmed by the study pathologist or his designate) after completion of definitive focal +/ - craniospinal irradiation , or must be a patient with first recurrence/disease progression who is unable to receive radiation therapy due to genetic disorders that put them at significant risk for radiation -induced secondary malignancies (ie. Gorlin’s syndrome or NF1 mutation) . Performance Stat us: The patient must have a KPS of > 50% (KPS for > 16 years of age) or Lansky performance Score (L P S ) o f ≥ 5 0 (L P S f o r ≤ 16 years of age) assessed within 2 weeks prior to registration and documented in the medical record or on SDW -UFBTIP -004. Patients who are unable to walk because of paralysis but who are up in a wheel chair will be considered ambulatory for the purposes of the performance score. Laboratory Analysis and Organ Function Requirements : Bone Marrow function: - Absolute neut rophil count ≥ 1000/µl (unsupported) * - Platelets ≥ 100,000/µl (unsupported) * - Hemoglobin > 8 g/dL (may be supported) *Patients on Group B with ANC <1000/µ L 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 . Renal : -Serum creatinine ≤ upper limit of institutional normal .