-  INCLUSION CRITERIA:

        2.1.1.1 Multiple Myeloma criteria

          -  Clear B-cell maturation antigen (BCMA) expression must be detected on greater than 50%
             of malignant plasma cells from either bone marrow or a plasmacytoma by flow cytometry
             or immunohistochemistry. These assays must be performed at the National Institutes of
             Health. It is not required that the specimen used for BCMA determination comes from a
             sample that was obtained after the patient's most recent treatment. BCMA expression
             will need to be documented on the majority of malignant plasma cells at some time
             after the original anti-BCMA chimeric antigen receptor (CAR) T-cell infusion in all
             patients undergoing a second anti-BCMA CAR T-cell infusion. If paraffin embedded
             unstained samples of bone marrow involved with multiple myeloma (MM) or a plasmacytoma
             are available, these can be shipped to the National Institutes of Health (NIH) for
             BCMA staining, otherwise new biopsies will need to be performed for determination of
             BCMA expression.

          -  Bone marrow plasma cells must make up 30% or less of total bone marrow cells based on
             a bone marrow biopsy performed within 30 days of the start of protocol treatment.

          -  Patients must have received at least 3 different prior treatment regimens for multiple
             myeloma

          -  Patients must have measurable MM as defined by at least one of the criteria below.

             a. One or more of these abnormalities defines measurable disease:

               -  Serum M-protein greater or equal to 1 g/dl (10 g/l).

               -  Urine M-protein greater or equal to 200 mg/24 h.

               -  Serum free light chain (FLC) assay: involved FLC level greater or equal to10
                  mg/dl (100 mg/l) provided serum FLC ratio is abnormal.

               -  A biopsy-proven plasmacytoma

          -  Patients must have multiple myeloma that meets the criteria for one of the following
             Disease categories: (1) progressive disease or (2) relapse from Complete Remission
             (CR) as described in the International Uniform Response Criteria for Multiple Myeloma
             and as listed below.

               1. Progressive Disease (which requires 1 or more of the following)(A):

                  Increase of greater than or equal to 25% from the lowest response value (nadir)
                  in any one or more of these parameters:

                    1. Serum M-component (the absolute increase must be greater than or equal to
                       0.5 g/dL) (B) and/or

                    2. Urine M-component and/or (the absolute increase must be greater than or
                       equal to 200 mg/24 h)

                    3. Only in patients without measurable serum and urine M-protein levels; the
                       difference between involved and uninvolved FLC levels. The absolute increase
                       must be > 10 mg/dL.

                    4. Bone marrow plasma cell percentage; the absolute percentage must be greater
                       than or equal to 10%

          -  Definite development of new bone lesions or soft tissue plasmacytomas or definite
             increase in the size of existing bone lesions or soft tissue plasmacytomas (defined as
             50% or greater increase in the sum of the products of the cross-diameters of target
             lesions)

          -  Development of hypercalcemia (corrected serum calcium > 11.5 mg/dL or 2.65 mmol/L)
             that can be attributed solely to the plasma cell proliferative disorder

             2. Relapse from complete remission (A)

          -  Defined as one or more of the following; must be attributable to myeloma:

               1. Reappearance of serum or urine M-protein by immunofixation or electrophoresis

               2. Development of greater than or equal to 5% plasma cells in the bone marrow

               3. Appearance of any other sign of progression (i.e., new plasmacytoma, lytic bone
                  lesion, or hypercalcemia)

        (A)All relapse and progression categories require two consecutive assessments made at any
        time before classification as relapse or disease progression and/or the institution of any
        new therapy.

        (B)For progressive disease, serum M-component increases of greater than or equal to 1 gm/dL
        are sufficient to define progression if starting M-component is greater than or equal to 5
        g/dL.

        2.1.1.2 Other inclusion criteria:

          -  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 Eastern Cooperative Oncology Group (ECOG) 0-2

          -  Patients of both genders must be willing to practice birth control from the time of
             enrollment on this study and for four months after receiving the preparative regimen.

          -  Women of child bearing potential must have a negative pregnancy test because of the
             potentially dangerous effects of the preparative chemotherapy on the fetus.

          -  Seronegative for human immunodeficiency virus (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.)

          -  Seronegative for hepatitis B antigen, positive hepatitis B tests can be further
             evaluated by confirmatory tests, and if confirmatory tests are negative, the patient
             can be enrolled.

          -  Seronegative for hepatitis C antibody unless antigen negative. If hepatitis C antibody
             test is positive, then patients must be tested for the presence of antigen by Reverse
             transcription polymerase chain reaction (RT-PCR) and be hepatitis C virus (HCV)
             ribonucleic acid (RNA) negative.

          -  Absolute neutrophil count greater than or equal to 1000/mm^3 without the support of
             filgrastim or other growth factors.

          -  Platelet count greater than or equal to 45,000/mm^3 without transfusion support

          -  Hemoglobin greater than 8.0 g/dl.

          -  Less than 5% plasma cells in the peripheral blood leukocytes

          -  Serum alanine transaminase (ALT) and aspartate transaminase (AST) less or equal to 2.5
             times the upper limit of the institutional normal.

          -  Serum creatinine less than or equal to 1.3 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).

          -  Because this protocol requires collection of autologous blood cells by leukapheresis
             in order to prepare anti-BCMA-CAR 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 2 weeks 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 within 6 weeks of the start of the treatment protocol.

          -  Patients should not take corticosteroids including prednisone, dexamethasone or any
             other corticosteroid for any purpose at doses higher than 5 mg/day of prednisone or
             equivalent dose of another corticosteroid 2 weeks before apheresis and within 2 weeks
             prior to CAR T-cell infusion, and at any time after the CAR T cell infusion.

        2.1.2 EXCLUSION CRITTERIA:

          -  Patients on any anticoagulants except aspirin are not eligible.

          -  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.

          -  Active systemic infections (defined as infections causing fevers or requiring
             antimicrobial treatment), active coagulation disorders or other major uncontrolled
             medical illnesses of the cardiovascular, respiratory, endocrine, renal,
             gastrointestinal, genitourinary or immune system, history of myocardial infarction,
             active cardiac arrhythmias, 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 are not allowed within 2 weeks prior to
             either the required leukapheresis or the initiation of the conditioning chemotherapy
             regimen.

          -  History of severe immediate hypersensitivity reaction to any of the agents used in
             this study.

          -  History of allogeneic stem cell transplantation

          -  Patients with central nervous system (CNS) metastases or symptomatic CNS involvement
             (including cranial neuropathies or mass lesions and spinal cord compression).

          -  Patients with active autoimmune skin diseases such as psoriasis or other active
             autoimmune diseases such as rheumatoid arthritis.