Gene Modified Immune Cells After Conditioning Regimen for the Treatment of Stage IIIC or IV Melanoma or Metastatic Solid Tumors

Inclusion Criteria: * Histologically confirmed malignancy that is considered surgically incurable with either: * Stage IIIC melanoma including locally relapsed, satellite, in-transit lesions or bulky draining node metastasis * Stage IV melanoma including patients with known brain metastases * Other metastatic, non-central nervous system (CNS) solid tumor relapsed or refractory after all standard-of-care systemic therapies for which the patient is eligible * Confirmed IL13Ralpha2 tumor expression by immunohistochemistry (immunohistochemical assay \[IHA\] H-Score \>= 50 in at least 10% of the total tumor specimen and in at least two high-power fields) * Age greater than or equal to 18 years old and less than 75 years old * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * A minimum of one measurable lesion defined as: * Meeting the criteria for measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST), OR * Skin lesion(s) selected as non-completely biopsied target lesion(s) that can be accurately measured and recorded by color photography with a ruler to document the size of the target lesion(s) * Absolute neutrophil count (ANC) \>= 1 x 10\^9 cells/L (determined within 30-60 days prior to enrollment; re-evaluated within 14 days of beginning conditioning chemotherapy) * Platelets \>= 75 x 10\^9/L (determined within 30-60 days prior to enrollment; re-evaluated within 14 days of beginning conditioning chemotherapy) * Hem…