Inclusion Criteria:

          -  Participant has treated leptomeningeal metastases after intrathecal chemotherapy
             and/or radiation OR refuses to undergo radiation and/or intrathecal chemotherapy

          -  Participant must have a Karnofsky performance status (KPS) >= 60

          -  Participant must have a life expectancy of >= 8 weeks

          -  If participant has a ventriculoperitoneal shunt, the valve must be programmable, and
             must be able to tolerate their shunts being turned off for 48 hours

          -  The effects of IL13Ralpha2-CAR T cells on a developing fetus are unknown. For this
             reason, 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 IL13Ralpha2+ tumor expression by
             immunohistochemistry (IHC) at the initial tumor presentation or recurrent disease
             (H-score >= 50)

          -  Participant 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%
             and the situation is not expected to resolve within 2 weeks

          -  Research participant requires dialysis

          -  Research participant has uncontrolled seizure activity and/or clinically evident
             progressive encephalopathy

          -  Failure of research participant to understand the basic elements of the protocol
             and/or the risks/benefits of participating in this phase 1 study. A legal guardian may
             substitute for the research participant

          -  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 IL13Ralpha2-CAR T
             cell study

          -  Shunted participants either have a non-programmable shunt valve, or cannot tolerate
             their shunts being turned off for 48 hours

          -  Participant has a coagulopathy or bleeding disorder or cannot safely discontinue
             anticoagulation prior to placement of a Rickham reservoir

          -  Participant has a chronic or active viral infection of the central nervous system
             (CNS)

          -  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 is human immunodeficiency virus (HIV) seropositive based on testing
             performed within 4 weeks of signing the main informed consent

          -  Participant has an autoimmune disease

          -  Participant has another active malignancy

          -  Participant is unable to undergo a brain magnetic resonance imaging (MRI)

          -  Participant is pregnant or breast feeding. Because there is an unknown but potential
             risk for adverse events in nursing infants secondary to treatment of the mother with
             IL13Ralpha2-CAR T cells, breastfeeding should be discontinued if the mother wants to
             participate in this study

          -  Prospective participants who, in the opinion of the Investigator, may not be able to
             comply with all study procedures (including compliance issues related to
             feasibility/logistics)