The following criteria is provided for health care professionals.

INCLUSION CRITERIA - MULTIPLE MYELOMA:

• SLAMF7 expression must be detected on malignant plasma cells from either bone marrow or a plasmacytoma by flow cytometry or immunohistochemistry. A specific quantitative level of SLAMF7 expression for eligibility is not specified, but patients with multiple myeloma cells that are negative for SLAMF7 by flow cytometry and immunohistochemistry will not be enrolled. These assays must be performed at the National Institutes of Health (NIH). It is not required that the specimen used for SLAMF7 determination comes from a sample that was obtained after the patient s most recent treatment. If paraffin embedded unstained samples of bone marrow involved with MM or a plasmacytoma are available, these can be shipped to the NIH for SLAMF7 staining, otherwise new biopsies will need to be performed for determination of SLAMF7 expression.
• SLAMF7 expression will need to be documented on the majority of malignant plasma cells by flow cytometry at the NIH at some time after the original CAR-SLAMF7 T-cell infusion in all patients undergoing a second CAR-SLAMF7 T-cell infusion on this clinical trial .
• Bone marrow plasma cells must make up less than or equal to 50% of total bone marrow cells based on a bone marrow biopsy performed within 21 days of the start of protocol treatment.
• Patients must have received at least 3 different prior treatment regimens for multiple myeloma
• Must have prior exposure to an immunomodulatory drug (IMiD) such as lenolidamide and a proteasome inhibitor
• Patients must have measurable MM as defined by at least one of the criteria below.
  • Serum M-protein greater or equal to 1.0 g/dL.
  • Urine M-protein greater or equal to 200 mg/24 h.
  • Serum free light chain (FLC) assay: involved FLC level greater or equal to 10 mg/dL (100 mg/L) provided serum FLC ratio is abnormal.
  • A biopsy-proven plasmacytoma at least 1.5 cm in largest dimension
  • Bone marrow core biopsy with 30% or more plasma cells

INCLUSION CRITERIA - OTHER:

• Greater than or equal to 18 years of age and less than or equal to age 73.
• Able to understand and sign the Informed Consent Document.
• Clinical performance status of ECOG 0-2
• Patients of both sexes must be willing to practice birth control from the time of enrollment on this study and for four months after last day of receiving protocol treatment.
• Seronegative for HIV antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus are less responsive to the experimental treatment and more susceptible to its toxicities.)
• A patient with a negative blood PCR test for hepatitis B DNA test can be enrolled. If hepatitis B DNA (PCR) testing is not available, patients with a negative hepatitis B surface antigen and negative hepatitis B core antibody can be enrolled.
• Patients must be tested for the presence of Hepatitis C antigen by PCR and be HCV RNA negative in order to be eligible. Only if Hepatitis C PCR testing is not available in a timely manner, patients who are Hepatitis C antibody-negative can be enrolled.
• Absolute neutrophil count greater than or equal to 1000/mm^3 without the support of filgrastim or other growth factors within the previous 10 days.
• Platelet count greater than or equal to 55,000/mm^3 without transfusion support in the past 14 days.
• Hemoglobin greater than or equal to 8.0 g/dL.
• Less than 5% plasma cells in the peripheral blood leukocytes
• Serum ALT and AST less or equal to 2.5 times the upper limit of the institutional normal.
• Serum creatinine less than or equal to 1.5 mg/dL.
• Total bilirubin less than or equal to 2.0 mg/dL, except in patients with Gilbert's Syndrome who must have a total bilirubin less than 3.0 mg/dL.
• At least 14 days must have elapsed since any prior systemic therapy at the time the patient starts the cyclophosphamide and fludarabine conditioning regimen, and patients toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo or cytopenias).
• Because this protocol requires collection of autologous blood cells by leukapheresis in order to prepare CAR-SLAMF7 T cells, systemic anti-myeloma therapy including systemic corticosteroid steroid therapy of greater than 5 mg/day of prednisone or equivalent dose of another corticosteroid are not allowed within 14 days prior to the required leukapheresis.
• Normal cardiac ejection fraction (greater than or equal to 50% by echocardiography) and no evidence of hemodynamically significant pericardial effusion as determined by an echocardiogram.
• For patients with past participation in gene-therapy, cryopreserved PBMC that have not been genetically-engineered must be available.
• Patients receiving prior gene therapy outside of NIH will not be eligible. Patients who previously received CAR T-cell therapy at the NCI will be potentially eligible.

EXCLUSION CRITERIA:

• Patients who are receiving any other investigational agents.
• Patients on any anticoagulants except aspirin
• Patients that require urgent therapy due to tumor mass effects or spinal cord compression.
• Patients that have active hemolytic anemia.
• Patients with second malignancies in addition to multiple myeloma are not eligible if the second malignancy has required treatment within the past 3 years or is not in complete remission. There are two exceptions to this criterion: successfully treated non-metastatic basal cell or squamous cell skin carcinoma.
• Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. Women of child bearing potential cannot have a positive pregnancy test. Women of childbearing potential are defined as all women except women who are post-menopausal or who have had a hysterectomy. Postmenopausal will be defined as women over the age of 55 who have not had a menstrual period in at least 1 year.
• Active systemic infections (defined as infections causing fevers or requiring anti-microbial treatment), active coagulation disorders or other major uncontrolled illnesses of the cardiovascular, respiratory, endocrine, renal, gastrointestinal, genitourinary, neurologic, psychiatric, or immune system, history of myocardial infarction, active cardiac arrhythmias, history of atrial fibrillation or other arrhythmias other than sinus tachycardia, active obstructive or restrictive pulmonary disease.
• Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease).
• Systemic corticosteroid steroid therapy of greater than 5 mg/day of prednisone or equivalent dose of another corticosteroid (prednisone, dexamethasone, etc.) is not allowed within 14 days prior to either the required leukapheresis or within 14 days prior to CAR Tcell infusion (and at any time after the CAR T cell infusion unless approved by the Principal Investigator or an Associate Investigator).
• History of severe immediate hypersensitivity reaction to any of the agents used in this study.
• Patient unwilling to undergo intensive care unit treatment including mechanical ventilation, cardiopulmonary resuscitation, vasoactive drugs, and hemodialysis.
• History of allogeneic stem cell transplantation
• Patients with currentspinal cord compression (without intradural myeloma involvement.
• Patients who have a history (or current evidence) of cerebrospinal fluid multiple myeloma, or intra-dural central nervous system masses.
• Patients with active autoimmune skin diseases such as psoriasis or other active autoimmune diseases such as rheumatoid arthritis.
• Patients must not have required supplemental oxygen within the past month unless it was for a resolved infection.