Multicenter Open Label Phase 2 Study of Isatuximab Plus Pomalidomide and Dexamethasone With Carfilzomib in Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: 1. Must be able to understand and voluntarily sign an informed consent form 2. Must be able to adhere to the study visit schedule and other protocol requirements 3. Male or female, age 18 years or older 4. Life expectancy of \> 6 months. 5. Must have a in R1 and R2 relapse Multiple Myeloma with a measurable disease : * 1 to maximum 2 lines of therapy prior to study entry * Relapse Refractory or primary refractory or relapse * Must have received prior treatment with a Lenalidomide-containing regimen for at least 2 consecutive cycles 6. Must have measurable disease as defined by the following: must have a clearly detectable and quantifiable monoclonal M-component value in the serum and/or urine : * IgG/IgA (serum M-component \> 5g/l), * Light chain (serum M-component \>1g/l or Bence Jones \> 200mg/24H), * Serum FLC assay (including for IgD isotypes): involved FLC level \> 10 mg/dl provided serum. FLC ratio is abnormal for patients not measurable on any of the 3 above criteria. 7. Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1, or 2 8. Wash out period without MM treatment must be of 28 days minimum before C1D1, except for anti CD-38 (See exclusion criteria#10). 9. Adequate bone marrow function, documented within 72 hours and without transfusion 72 hours prior to the first intake of investigational product (C1J1) with no growth factor support (one week), defined as : * Absolute neutrophils ≥ 1 x109/L, * Untransfused Platelet count ≥ 75 x109/L, * Hemoglobin ≥ 8.5 g/dL. 10. Adequate organ function defined as : * Serum total bilirubin \< 2x upper limit of normal (ULN), * Clearance creatinine ≥ 30ml/min, * Serum SGOT/AST or SGPT/ALT \< 3x upper limit of normal (ULN). 11. Patients affiliated to an appropriate social security system. 12. A man who is sexually active with a pregnant female or a FCBP\* must agree to use a barrier method of birth control eg, condom with spermicidal foam/gel/film/cream/suppository, even if he has had a vasectomy. All men must also not donate sperm, spermatozoa during the study, for 5 months following treatment discontinuation. 13. A woman FCBP\* must understand and agree to use 2 reliable effective methods (a very effective method and an effective additional method) of contraception simultaneously without interruption : * For at least 28 days before starting experimental treatments, * Throughout the entire duration of experimental treatments, * During dose interruptions, * And for at least 5 months after the last dose of experimental treatments. 14. All patients must agree to not donate blood during the treatment period, interruptions of treatment and at least 5 months after the last dose of treatment. 15. All patients must understand and accept to comply with the conditions of the Pomalidomide pregnancy prevention plan (Appendix of the protocol). Exclusion Criteria: 1. Any other uncontrolled medical condition or comorbidity that might interfere with patient's participation, including simultaneous participation to another interventional clinical study. 2. Known positive for HIV or active infectious hepatitis, type B or C. 3. Patients with non-secretory MM and non-measurable MM 4. Patient with terminal renal failure that require dialysis or clearance creatinine \< 30 ml/min (calculated with MDRD formula) 5. Any uncontrolled or severe cardiovascular or pulmonary disease determined by the investigator including : * NYHA functional classification III or IV congestive heart failure * LVEF (Left Ventricular Ejection Fraction) \< 40% * Uncontrolled angina, hypertension or arrhythmia * Myocardial infarction in the past 6 months 6. Prior history of malignancies, other than multiple myeloma, unless the patients has been free of the disease for ≥ 5 years. Exceptions include the following: * Basal or squamous cell carcinoma of the skin * Carcinoma in situ of the cervix or breast * Incidental histologic finding of prostate cancer (TNM stage of T1a or T1b) 7. Evidence of central nervous system (CNS) involvement 8. Ongoing active infection or other clinically significant uncontrolled cardiovascular events 9. Unable to comply with IMids regulation to thromboprophylaxis, or teratogenic recommandations. 10. Refractory to prior to anti CD38.Patients can be exposed to anti CD38 (any), BUT the wash out period for patient pre-treated with an anti CD38 antibody must be of 4,5 months minimum between last dose of previous anti-CD38 antibody and the first dose of isatuximab. 11. Refractory to prior carfilzomib 12. Known allergy to one of the study product (pomalidomide, isatuximab, carfilzomib) or dexamethasone 13. Patient with a history of severe allergic reactions to thalidomide or lenalidomide 14. Exposed to pomalidomide 15. Known intolerance to infused protein products, sucrose, histidine, and PS80 16. Contraindications to dexamethasone 17. Any ongoing non hematological adverse event or medical history grade\> 2 severity 18. Pregnant or breast-feeding females 19. Refusal to participate in the study 20. Persons protected by a legal regime (guardianship, trusteeship)