Inclusion Criteria:

          -  Histologically confirmed melanoma 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

          -  Confirmed IL13Ralpha2 tumor expression by immunohistochemistry (>= 20%, 1+)

          -  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)

          -  Hemoglobin >= 8 g/dL (determined within 30?60 days prior to enrollment; re-evaluated
             within 14 days of beginning conditioning chemotherapy)

          -  Aspartate and alanine aminotransferases (AST, ALT) =< 2.5 x upper limit of normal
             (ULN) (determined within 30?60 days prior to enrollment; re-evaluated within 14 days
             of beginning conditioning chemotherapy)

          -  Total bilirubin =< 2 x ULN (except patients with documented Gilbert?s syndrome)
             (determined within 30?60 days prior to enrollment; re-evaluated within 14 days of
             beginning conditioning chemotherapy)

          -  Creatinine < 2 mg/dL (or a glomerular filtration rate > 45) (determined within 30?60
             days prior to enrollment; re-evaluated within 14 days of beginning conditioning
             chemotherapy)

          -  Must have received at least one prior systemic therapy for advanced melanoma (i.e.
             anti-PD-1 therapy, BRAF plus MEK inhibitor therapy for BRAFV600 mutated melanoma) and
             is not considered to have an alternate treatment option with curative intent

          -  Must be willing and able to accept at least one leukapheresis procedure

          -  Must be willing and able to provide written informed consent

        Exclusion Criteria:

          -  Inability to purify >= 1 x 10^7 T cells from leukapheresis product

          -  Previously known hypersensitivity to any of the agents used in this study; known
             sensitivity to cyclophosphamide or fludarabine

          -  Received systemic treatment for cancer, including immunotherapy, within 14 days prior
             to initiation of conditioning chemotherapy administration within this protocol

          -  Potential requirement for systemic corticosteroids or concurrent immunosuppressive
             drugs based on prior history or received systemic steroids within the last 2 weeks
             prior to enrollment (inhaled or topical steroids at standard doses are allowed)

          -  Human immunodeficiency virus (HIV) seropositivity or other congenital or acquired
             immune deficiency state, which would increase the risk of opportunistic infections and
             other complications during chemotherapy-induced lymphodepletion. If there is a
             positive result in the infectious disease testing that was not previously known, the
             patient will be referred to their primary physician and/or infectious disease
             specialist

          -  Hepatitis B or C seropositivity with evidence of ongoing liver damage, which would
             increase the likelihood of hepatic toxicities from the chemotherapy conditioning
             regimen and supportive treatments. If there is a positive result in the infectious
             disease testing that was not previously known, the patient will be referred to their
             primary physician and/or infectious disease specialist

          -  Dementia or significantly altered mental status that would prohibit the understanding
             or rendering of informed consent and compliance with the requirements of this protocol

          -  A Tiffeneau-Pinelli index < 70% of the predicted value. Subjects will be excluded if
             pulmonary function tests indicate they have insufficient pulmonary capability

          -  Patients will be excluded if they have a history of clinically significant
             electrocardiography (ECG) abnormalities, symptoms of cardiac ischemia or arrhythmias
             and have a left ventricular ejection fraction (LVEF) < 45% on a cardiac stress test
             (stress thallium, stress multigated acquisition scan (MUGA), dobutamine
             echocardiogram, or other stress test)

          -  Patients with ECG results of any conduction delays (PR interval > 200 ms, corrected QT
             (QTC) > 480 ms), sinus bradycardia (resting heart rate < 50 beats per minute), sinus
             tachycardia (HR>120 beats per minute) will be evaluated by a cardiologist prior to
             starting the trial. Patients with any arrhythmias, including atrial
             fibrillation/atrial flutter, excessive ectopy (defined as > 20 premature ventricular
             complex [PVC]s per minute), ventricular tachycardia, 3rd degree heart block will be
             excluded from the study unless cleared by a cardiologist

          -  Pregnancy or breast-feeding. Female patients must be surgically sterile or be
             postmenopausal for two years, or must agree to use effective contraception during the
             period of treatment and for 6 months afterwards. All female patients with reproductive
             potential must have a negative pregnancy test (serum/urine) at screening and again
             within 14 days from starting the conditioning chemotherapy. The definition of
             effective contraception will be based on the judgment of the study investigators.
             Patients who are breastfeeding are not allowed on this study

          -  A concomitant active malignancy that would be considered to interfere with the
             assessment of the primary or secondary endpoints of the study