Inclusion Criteria:

          -  Histopathologic documentation (must be performed or reviewed at MD Anderson) of
             recurrent high grade epithelial ovarian cancer.

          -  At least one prior line of platinum-based chemotherapy (subjects are eligible for
             enrollment and leukapheresis while still platinum-sensitive, however, they must have
             developed platinum resistant disease for treatment (turnstile 2).

          -  Tumor expressing PRAME and/or COL6A3.

          -  Expression of HLA-A*0201.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.

          -  Expected survival of greater than 16 weeks.

          -  Willing and able to give informed consent.

          -  Hemoglobin >= 9.0 g/dL.

          -  Absolute neutrophil count (ANC) >= 1.0 x 10^9/L (>=1000 per mm^3).

          -  Platelet count >= 75 x 10^9/L (>=100,000 per mm^3).

          -  Serum bilirubin =< 1.5 x institutional upper limit of normal (ULN) unless diagnosed
             with Gilbert's syndrome.

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN
             unless liver metastases are present, in which case it must be =< 5x ULN.

          -  Serum creatinine clearance (CL) >40 mL/min by the Cockcroft-Gault formula or by
             24-hour urine collection for determination of creatinine clearance.

          -  Subjects must either be of non-reproductive potential (i.e., post-menopausal by
             history: >= 50 years old and no menses for >=1 year without an alternative medical
             cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history
             of bilateral oophorectomy) or must have a negative serum pregnancy test upon study
             entry.

          -  Women of childbearing potential (WOCBP) must be using an adequate method of
             contraception to avoid pregnancy throughout the study in such a manner that the risk
             of pregnancy is minimized. Suggested precautions should be used to minimize the risk
             or pregnancy for at least 1 month before start of therapy, and while women are on
             study for up to 3 months after T cell infusion, and at least 8 weeks after the study
             drug is stopped.

          -  {Turnstile 2} Subjects must have platinum resistant disease (progression on a
             platinum-containing regimen or recurrence within 180 days of last dose of
             platinum-containing chemotherapy). Subjects that are not platinum resistant but are
             deemed not to be candidates for platinum-based chemotherapy due to prior significant
             allergic reaction may participate with principal investigator (PI) approval.

          -  {Turnstile 2} Bi-dimensionally measurable disease by radiographic imaging (magnetic
             resonance imaging [MRI] or computed tomography [CT] scan).

          -  {Turnstile 2} At least 4 weeks must have elapsed since the last chemotherapy,
             immunotherapy, radiotherapy or major surgery. At least 6 weeks for bevacizumab.

          -  {Turnstile 2} Toxicity related to prior therapy must either have returned to =< grade
             1, baseline, or been deemed irreversible.

        Exclusion Criteria:

          -  Clinically significant pulmonary dysfunction, as determined by medical history and
             physical exam. Patients so identified will undergo pulmonary functions testing and
             those with forced expiratory volume in one second (FEV1) < 60% of normal or carbon
             monoxide diffusing capacity (DLco) (corrected [corr] for hemoglobin [Hgb]) < 55% will
             be excluded.

          -  Significant cardiovascular abnormalities including any one of the following:
             Congestive heart failure, Clinically significant hypotension, symptoms of coronary
             artery disease, presence of cardiac arrhythmias on electrocardiography (EKG) requiring
             drug therapy; or patients with a history of cardiovascular disease. (Patients with the
             above will undergo a cardiac evaluation which can include a stress test and/or
             echocardiography. Results of this evaluation will be considered before excluding
             patients on the basis of cardiovascular abnormalities). Subjects with evidence of
             stress-induced cardiac ischemia or ejection fraction less than 55% will be excluded.

          -  History of central nervous system (CNS) metastasis.

          -  Autoimmune disease: patients with a history of inflammatory bowel disease are excluded
             from this study, as are patients with a history of autoimmune disease (e.g. systemic
             lupus erythematosus, vasculitis, infiltrating lung disease) whose possible progression
             during treatment would be considered by the Investigator to be unacceptable.

          -  {Turnstile 2} Participation in another clinical study with an investigational product
             administered during the last 28 days.

          -  {Turnstile 2} Receipt of the last dose of previous chemotherapy, hormonal, or biologic
             treatment for ovarian, fallopian tube, or primary peritoneal cancer in the last 28
             days (in the last 6 weeks for bevacizumab).

          -  {Turnstile 2} Current or prior use of immunosuppressive medication within 28 days
             before enrollment, with the exceptions of intranasal and inhaled corticosteroids or
             systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of
             prednisone, or an equivalent corticosteroid.

          -  {Turnstile 2} Any prior grade >= 3 immune-related adverse event (irAE) while receiving
             any previous immunotherapy agent, or any unresolved irAE > grade 1.

          -  History of allogeneic organ transplant.

          -  Unresolved partial or complete small or large bowel obstruction.

          -  {Turnstile 2} Receipt of live attenuated vaccination within 30 days prior to
             enrollment or within 30 days of planned lymphodepletion.

          -  Any underlying medical or psychiatric condition, which in the opinion of the
             investigator, will make the administration of study drug hazardous or obscure the
             interpretation of adverse events.

          -  Active viral hepatitis.

          -  Confirmed human immunodeficiency virus (HIV) infection.