Inclusion Criteria:

          -  Histopathologic documentation of synovial sarcoma or myxoid liposarcoma with the
             diagnosis of advanced or recurrent disease who have received prior standard
             chemotherapy. Patients with other sarcoma subtypes if proven to be NY-ESO-1 positive
             and meeting all other eligibility criteria listed below will also be included.

          -  Tumor expression of NY-ESO-1 (2+ staining or > 25%) by immunohistochemistry (IHC).

          -  Expression of HLA-A*0201.

          -  Eastern Cooperative Oncology Group (ECOG)/ Zubrod performance status of '0-1'

          -  Life expectancy > 6 months.

          -  Electrocardiography (ECG) without evidence of clinically significant arrhythmia or
             ischemia.

          -  Women of childbearing potential (WOCBP) must be using at least one highly effective or
             two effective accepted methods of contraception to avoid conception 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/or
             at least 3 months after the study agents LV305 or CMB305 are stopped. WOCBP include
             any female who has experienced menarche and who has not undergone successful surgical
             sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is
             not postmenopausal.

          -  Men must be willing and able to use an acceptable method of birth control such as
             latex condom during the dosing period and for at least 3 months after completion of
             the study agent administration (T cell infusion and/or LV305 or CMB305) if their
             sexual partners are WOCBP.

          -  Willing and able to give informed consent.

          -  (Prior to treatment) Note: evaluate at least 1 week before T cell infusion. a.
             Adequate venous access - consider peripherally inserted central catheter (PICC) or
             central line. b. ECOG/Zubrod performance status of '0-1. c. Bi-dimensionally
             measurable disease by palpation on clinical exam, or radiographic imaging (X-ray,
             computed tomography [CT scan]). d. At least 4 weeks must have elapsed since the last
             chemotherapy, immunotherapy, radiotherapy or major surgery. At least 6 weeks for
             nitrosoureas, mitomycin C and liposomal doxorubicin. e. Toxicity related to prior
             therapy must either have returned to =< grade 1, baseline, or been deemed
             irreversible. f. Persons of reproductive potential must agree to use and utilize an
             adequate method of contraception throughout treatment and for at least 3 months after
             study drug is stopped. g. Willing and able to give informed consent.

        Exclusion Criteria:

          -  Patients with active infections or oral temperature > 38.2 Celsius (C) within 72 hours
             of leukapheresis. The procedure may be deferred.

          -  Investigational therapy within 3 weeks.

          -  Prior administration of other NY-ESO-1 targeting immunotherapeutics.

          -  Significant immunosuppression from concurrent, recent (=< 4 weeks ago) or anticipated
             treatment with systemic corticosteroids at any dose, or other immunosuppressive
             medications such as methotrexate, cyclosporine, azathioprine (antihistamines,
             non-steroidal anti-inflammatory drugs and aspirin permitted) or conditions such as
             common variable hypogammaglobulinemia or exposures such as large field radiotherapy.

          -  Cancer therapies, including chemotherapy, radiation, biologic, or kinase inhibitors,
             granulocyte colony-stimulating factor (G-CSF), granulocyte-macrophage
             colony-stimulating factor (GM-CSF) within 3 weeks prior.

          -  Psychiatric, other medical illness or other condition that in the opinion of the
             principal investigator (PI) prevents compliance with study procedures or ability to
             provide valid informed consent.

          -  Significant autoimmune disease with the exception of alopecia, vitiligo,
             hypothyroidism or other conditions that have never been clinically active or were
             transient and have completely resolved and require no ongoing therapy.

          -  Myocardial infarction within 6 months of study initiation, active cardiac ischemia or
             New York Heart Association (NYHA) grade III or IV heart failure.

          -  Peripheral blood leukocyte count (white blood cells [WBC]) < 3000/mm^3.

          -  Absolute neutrophil count =< 1500/mm^3.

          -  Platelets < 75000/mm^3.

          -  Hemoglobin < 10 gm/dL.

          -  Alanine aminotransferase (ALT), and aspartate aminotransferase (AST) > 2.5 x upper
             limit of normal (ULN).

          -  Total serum bilirubin > 1.5 x ULN (patients with Gilbert's disease may be included if
             their total bilirubin is =< 3.0 mg/dL).

          -  Creatinine > 1.5 x ULN. If higher check 24hr clearance, if < 50 ml/min then patient
             will be excluded.

          -  INR (prothrombin time ratio) or partial thromboplastin time (PTT) > 1.5 x ULN (Please
             note: patients with hematopoietic cell transplantation (Hct) < 30%, WBC < 2500/mm/^3
             and platelets < 50,000/mm^3 immediately prior to leukapheresis. The procedure may be
             deferred.)

          -  History of other cancer within 3 years (except non-melanoma cutaneous malignancies and
             cervical carcinoma in situ).

          -  Positive screening tests for human immunodeficiency virus (HIV), hepatitis (Hep) B,
             Hep C, active tuberculosis or recent (< 2 week ago) clinically significant infection
             or evidence of active HIV, Hep B, or Hep C. (Note: If positive results are not
             indicative of true active or chronic infection, the patient can be treated.)

          -  Brain metastases considered unstable as: a. without confirmed stability over 60 days
             in patients previously treated with prior surgery or radiation; OR b. associated with
             symptoms and/or findings; OR c. requiring corticosteroids or anticonvulsants in the
             prior 60 days.

          -  Pregnant, planning to become pregnant, or breast feeding.

          -  Known allergy(ies) to any component of CMB305 or LV305.

          -  Men or women of reproductive ability who are unwilling to use effective contraception
             and women of childbearing potential who are unwilling to undergo pregnancy testing
             before and during the study.

          -  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 1 second (FEV1) < 2.0 L or carbon monoxide
             diffusing capability (DLco) (correlation for hemoglobin [corr for Hgb]) < 75% will be
             excluded.

          -  Significant cardiovascular abnormalities as defined by any one of the following: a.
             congestive heart failure, b. clinically significant hypotension, c. symptoms of
             coronary artery disease, d. presence of cardiac arrhythmias on electrocardiography
             (EKG) requiring drug therapy, e. ejection fraction < 50 % (dobutimine stress echo).

          -  Active and untreated 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.

          -  Steroids are not permitted 3 days prior to T cell infusion and concurrently during
             therapy.

          -  No prisoners or children will be enrolled on this study.