A Study of Carfilzomib, Lenalidomide, Dexamethasone and Daratumumab for Patients With Relapsed/Refractory Myeloma With Salvage Autologous Hematopoietic Cell Transplantation

Inclusion Criteria: * Patient must be capable, willing, and able to provide written, informed consent. * Age ≥ 18-years-old and \<= 75-years-old. * Histologic confirmation of multiple myeloma by the enrolling institution * Symptomatic myeloma that has progressed/relapsed after 1 to 3 prior lines of therapy * Patients who have received \<=1 cycle of therapy after most recent progression/relapse are eligible to enroll on study * Treatment of hypercalcemia or spinal cord compression or aggressively progressing myeloma with current or prior corticosteroids is permitted * Bisphosphonates are permitted * Concurrent or prior treatment with corticosteroids for indications other than multiple myeloma is permitted * Prior treatment with radiotherapy is permitted * Patients with measurable disease who received up to one cycle of any therapy within 60 days with a washout period of 4 weeks from last dose (on a trial or outside a trial) are eligible * Maintenance single agent imid (ie. lenalidomide or pomalidomide) or monoclonal antibody (ie. daratumumab) do not require the 4-week washout period * More than 2 x 10\^6 autologous CD34+ cells/kg cryopreserved. The graft may not be CD34+ selected or otherwise manipulated to remove tumor or other cells. The graft can be collected at the transplanting institution or by a referring center. * Planning to receive autologous HCT per institutional standards as part of standard of care. Eligibility for autologous HCT should be based on institutional guidelines. * However, at minimum all patients must meet the following criteria: * KPS greater than 70 * Cardiac left ventricular ejection fraction of greater than 40% * Calculated creatinine clearance of greater than 40 cc/min * AST and ALT of less than 2 x upper limit of normal * Direct bilirubin of less than 2 x upper limit of normal * Total bilirubin of less than 2 x upper limit of normal. If Total bilirubin is abnormal. Direct bilirubin of less than 2 x upper limit of normal * Measurable disease as defined by any of the following International Myeloma Working Group Criteria * Monoclonal serum peak of greater than 0.5 gms per deciliter * Measurable urine peak as defined by urine protein electrophoresis of greater than 100 mg per 24 hours * Serum FLC assay: involved FLC level ≥10 mg/dL provided serum FLC ratio is abnormal * Hemoglobin ≥ 8 g/dL (80 g/L) within 14 days prior to enrollment (subjects may be receiving red blood cell \[RBC\] transfusions in accordance with institutional guidelines) * Platelet count ≥ 50 × 109/L (≥ 30 × 109/L if myeloma involvement in the bone marrow is \> 50%) within 14 days prior to initial treatment (subjects may be receiving platelet transfusions in accordance with institutional guidelines) . * Women of childbearing potential (WOCBP) † must agree to ongoing pregnancy testing and to practice contraception as described in section 9.3 and required by the Revlimid REMS program. † A woman of childbearing potential is a sexually mature female who has not undergone a hysterectomy or bilateral oophorectomy or has not been naturally postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in the preceding 24 consecutive months). * Male subjects must agree to practice contraception * All study participants must be registered into the mandatory Revlimid REMS program and be willing and able to comply with the requirements of the REMS program. Exclusion Criteria: * Plasma cell leukemia (\>20% circulating plasma cells) during screening studies * POEMS syndrome * Pregnant or lactating females. Because there is a potential risk for adverse events nursing infants secondary to treatment of the mother with carfilzomib in combination with lenalidomide. These potential risks may also apply to other agents used in this study. * Uncontrolled hypertension or diabetes * Active hepatitis B or C infection * Patients with HBV core antibody positive, but HBV PCR negative are eligible if they are on medication for suppression of HBV reactivation * Patients with HCV antibody positive, but PCR negative are eligible. * Serologically positive HIV (testing required during screening) * Significant cardiovascular disease with NYHA Class III or IV symptoms, EF\<40% or hypertrophic cardiomyopathy, or restrictive cardiomyopathy, or myocardial infarction within 6 months prior to enrollment, or unstable angina, or unstable arrhythmia as determined by history and physical examination. Echocardiogram will be performed during screening evaluation. * Moderate or severe pulmonary hypertension defined as PASP \>50 mm Hg * Chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal. Note that FEV1 testing is required for participants suspected of having COPD and participants must be excluded if FEV1 is \< 50% of predicted normal. * Moderate or severe persistent asthma within the past 2 years, or uncontrolled asthma of any classification. Note that participants who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed to participate. * Refractory GI disease that would prevent absorption of oral agents * Uncontrolled intercurrent illness including but not limited to active infection or psychiatric illness/social situations that would compromise compliance with study requirements * Significant neuropathy ≥Grade 3 or Grade 2 neuropathy with pain at baseline * Contraindication to any concomitant medication, including antivirals or anticoagulation. * Major surgery within 3 weeks prior to first dose * Prior Allogeneic HCT (prior autologous transplant is allowed regardless of response) * History of CNS involvement by myeloma * Disease progression as defined by IMW Criteria1 on the combination of carfilzomib, lenalidomide and dexamethasone (Patients with progression on lenalidomide maintenance after completion of carfilzomib, lenalidomide and dexamethasone combination therapy will be eligible). * Disease progression on daratumumab * Prior dose limiting toxicity from carfilzomib or lenalidomide.