The Efficacy and Safety of Brain-targeting Immune Cells (EGFRvIII-CAR T Cells) in Treating Patients With Leptomeningeal Disease From Glioblastoma. Administering Patients EGFRvIII -CAR T Cells May Help to Recognize and Destroy Brain Tumor Cells in Patients

Inclusion Criteria: * Participant has been treated for leptomeningeal metastases after intrathecal chemotherapy and/or radiation OR refuses to undergo additional radiation and/or intrathecal chemotherapy * Participant must have a Karnofsky performance status (KPS) \>= 60 * Participant must have a life expectancy of \>= 2 months * Women of child-bearing potential must have negative serum pregnancy test and agree to use a reliable form of birth control prior to study entry and for at least two months following study treatment. Male research participants must agree to use a reliable form of birth control and not donate sperm during the study and for at least two months following study treatment * Participant has a histologically confirmed EGFRvII+ (epidermal growth factor receptor) tumor expression by immunohistochemistry (IHC) at the initial tumor presentation or recurrent disease (H-score \>= 50) * Participant or legal guardian must have the ability to understand and the willingness to sign a written informed consent Exclusion Criteria: * Research participant requires supplemental oxygen to keep saturation greater than 95% * Research participant requires dialysis * Research participant has uncontrolled seizure activity and/or clinically evident progressive encephalopathy * Failure of research participant or legal guardian to understand the basic elements of the protocol and/or the risks/benefits of participating in the study. * Participant is unwilling to stop treatment with chemotherapy or endocrine therapy and/or radiation one week prior and during the first 4 cycles of the study * Participant has ventriculoperitoneal shunt * Participant has a coagulopathy or bleeding disorder * Participant is HIV+ (human immunodeficiency virus) or has acute CMV (cytomegalovirus) infection * Participant has any uncontrolled illness, including ongoing or active infection; participant has known active hepatitis B or C infection; participants with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections * Participant has an autoimmune disease that requires constant treatment * Participant has another active malignancy * Participant is unable to undergo a brain magnetic resonance imaging (MRI) * Participant is pregnant or breast feeding