BCMA Targeted CAR T Cells With or Without Lenalidomide for the Treatment of Multiple Myeloma

Inclusion Criteria: * Patients must have histologically confirmed MM by MSKCC pathologist, with MM cells expressing BCMA, previously treated with 2+ prior lines of therapy including an IMiD and a PI, either with refractory, persistent, or progressive disease * Age ≥ 18 years of age * Creatinine ≤2.0 mg/dL, direct bilirubin ≤2.0 mg/dL, AST and ALT ≤3.0x upper limit of normal (ULN) * Adequate pulmonary function as assessed by ≥92% oxygen saturation on room air by pulse oximetry. * HGB≥7g/dl, ANC≥1,000/mm3, Platelet≥30,000/mm3 without transfusion or growth factor support for at least 1 week * M spike ≥0.5 g/dL or involved free light chain ≥10 mg/dL with an abnormal free light chain ratio Exclusion Criteria: * Karnofsky performance status \<70 * Pregnant or lactating women. Women and men of childbearing age should use effective contraception while on this study and continue for 1 year after all treatment is finished * Impaired cardiac function (LVEF \<40%) as assessed by ECHO or MUGA scan * Patients with following cardiac conditions will be excluded: * New York Heart Association (NYHA) stage III or IV congestive heart failure * Myocardial infarction ≤6 months prior to enrollment * History of clinically significant ventricular arrhythmia or unexplained syncope, not believed to be vasovagal in nature or due to dehydration * History of severe non-ischemic cardiomyopathy * Patients with HIV or active hepatitis B or hepatitis C infection are ineligible * Patients with any concurrent active malignancies as defined by malignancies requiring any therapy other than expectant observation or hormonal therapy, with the exception of squamous and basal cell carcinoma of skin * Patients with a prior allogeneic transplant ARE eligible UNLESS previously or currently experienced GvHD that required systemic steroids or other systemic lymphotoxic therapy * Patients on systemic steroids (except if solely for adrenal replacement) within two weeks of collection * Active auto-immune disease including connective tissue disease, uveitis, sarcoidosis, inflammatory bowel disease, or multiple sclerosis, or have a history of severe (as judged by the principal investigator) autoimmune disease requiring prolonged immunosuppressive therapy * Prior treatment with gene modified T cells * Prior or active CNS involvement by myeloma (eg leptomeningial disease). Screening for this, for example, by lumbar puncture, is only required if suspicious symptoms or radiographic findings are present * Plasma cell leukemia * Pre-existing (active or severe) neurologic disorders (e.g. pre-existing seizure disorder) * Active uncontrolled acute infections * Any other issue which, in the opinion of the treating physician, would make the patient ineligible for the study * Patients who previously had any intolerance to Lenalidomide 10 mg or who have a contraindication to Lenalidomide will not be eligibile for concominant treatment with Lenalidomide but will remain eligible for CAR T cell therapy without Lenalidomide.