Safety and Efficacy of MAGE-A3/A6 T Cell Receptor Engineered T Cells (KITE-718) in HLA-DPB1*04:01 Positive Adults With Advanced Cancers

Key Inclusion Criteria: * Age ≥ 18 years * Advanced cancer defined as relapsed or refractory disease after a systemic standard of care treatment regimen and, if available, at least one standard of care salvage regimen unless the subject refuses such therapy. Multiple myeloma (MM) subjects must have had both a protease inhibitor (PI) and immunomodulatory drugs (IMiD) as part of the last regimen, or at least 3 prior lines of therapy, including a PI and an IMiD. Additionally, subjects must not have disease amenable to definitive locoregional therapy. * MAGE-A3/A6 positive tumor as confirmed by the central laboratory * HLA-DPB1\*04:01 positive * At least 1 measurable lesion on CT or MRI * No evidence of central nervous system (CNS) disease by MRI or CT of the brain. Note: Prior brain metastasis which have been treated with definitive therapy are eligible provided that the definitive therapy was completed more than six months prior to screening. * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Toxicities due to prior therapy must be recovered to baseline or ≤ grade 1, except for clinically non-significant toxicities such as alopecia * Adequate bone marrow function as evidenced by: * Absolute neutrophil count (ANC) ≥ 1000/mm\^3 * Platelet ≥ 100/mm\^3 * Hemoglobin \> 8 g/dL * Adequate renal, hepatic, cardiac, and pulmonary function as evidenced by: * Creatinine clearance (as estimated by Cockcroft Gault) ≥ 60 cc/min (24-hour urine creatinine clearance is also acceptable) * Alanine transaminase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 x upper limit normal (ULN) or ≤ 5 x ULN if documented liver metastases * Total bilirubin ≤ 1.5 mg/dL * Cardiac ejection fraction ≥ 50%, no evidence of pericardial effusion as determined by an ECHO, and no clinically significant ECG findings (For ejection fraction only, MUGA scan is also acceptable) * No clinically significant pleural effusion * Baseline oxygen saturation \> 92% on room air Key Exclusion Criteria: * Malignancy other than non-melanoma skin cancer, carcinoma in situ, or low grade prostate cancer for which watch-and-wait approach is standard of care, unless disease free for at least 3 years * Clinically significant cardiac disease within last 12 months * Stroke or transient ischemic attack (TIA) within 12 last months * Symptomatic deep vein thrombosis or pulmonary embolism within last 6 months, catheter associated thrombosis is not included as exclusion criteria. * Prior T-cell therapy, including KITE-718 or MAGE-A3/A6-targeting therapy. * Live vaccine ≤ 4 weeks prior to enrollment * Systemic corticosteroid therapy within 7 days before enrollment. * History of severe, immediate hypersensitivity reaction attributed to aminoglycosides * Presence of fungal, bacterial, viral, or other infection requiring IV antimicrobials for management. * Presence of any indwelling line or drain. Note: Dedicated central venous access catheters such as a Port-a-Cath or Hickman catheter as well as feeding tubes such as a G-tube, are permitted. * Primary immunodeficiency * Autoimmune disease resulting in end-organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years prior to enrollment. * Known history of infection with HIV, hepatitis B (HBsAg positive), or hepatitis C (anti-HCV positive). A history of treated hepatitis B or hepatitis C is permitted if the viral load is undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing. * Females who are pregnant as confirmed by a positive serum or urine pregnancy test or are breastfeeding. * Individuals of both genders of child-bearing potential who are not willing to practice birth control from the time of consent through 6 months after the completion of KITE-718 Note: Other protocol defined Inclusion/Exclusion criteria may apply.