Carfilzomib, Pomalidomide, and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Relapsed and relapsed/refractory multiple myeloma requiring systemic therapy * Failed at least one prior treatment for multiple myeloma (must have received lenalidomide) * To be enrolled as second line therapy: Must be refractory to lenalidomide (progression on therapy or within 60 days of lenalidomide dosing) * Measurable disease, as indicated by one or more of the following: * Serum M-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg/24 hours * If serum protein electrophoresis is felt to be unreliable for routine M-protein measurement, then quantitative immunoglobulin levels are acceptable * Involved serum free light chains ≥ 10 mg/dL (free light change ratio must be abnormal) * Aged 18 years or older * Life expectancy of more than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Adequate Liver Function * Bilirubin \< 1.5 times the upper limit of normal (ULN) * Aspartate aminotransferase (AST) \< 2.5 times ULN * Alanine aminotransferase (ALT) \< 2.5 times ULN * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L * Hemoglobin \>= 8 g/dL * Platelet count \>= 75 x 10\^9/L (should be independent of platelet transfusions for at least 2 weeks) * Calculated or measured creatinine clearance of \>= 30 mL/minute * Written informed consent * Negative pregnancy test (for women of childbearing potential) within 10-14 days of starting study treatment and again within 24 hours of first pomalidomide dose * Must agree to practice abstinence or use two acceptable methods of birth control * Men must agree to use latex condom during sexual contact with women of childbearing potential (even if post vasectomy) * Must agree to adhere to all study requirements, visit schedule, outpatient treatment, required concomitant medications, and laboratory monitoring * Must register to mandatory POMALYST REMS™ program and be willing and able to comply with the requirements of the POMALYST REMS™ program Exclusion Criteria: * Patients for whom there is the prospect of stem cell transplantation in the next 6 months in the treatment plan are excluded * POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Plasma cell leukemia * Waldenström's macroglobulinemia or immunoglobulin M (IgM) myeloma * Radiotherapy to multiple sites or immunotherapy within 4 weeks before start of protocol treatment (localized radiotherapy to a single site at least 1 week before start is permissible) * Participation in an investigational therapeutic study within 3 weeks or within 5 drug half lives (t1/2) prior to first dose, whichever time is greater * Patients known to be refractory to any proteasome inhibitor other than bortezomib or carfilzomib * Pregnant or lactating * History of allergy to mannitol or prior hypersensitivity to thalidomide, lenalidomide or pomalidomide * Major surgery within 3 weeks prior to first dose, * Prior peripheral stem cell transplant within 12 weeks of study enrollment * Has received any anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal (with the exception of hormones for thyroid conditions or estrogen replacement therapy \[ERT\]), or any investigational therapy within 21 days of enrollment * Myocardial infarction within 6 months prior to enrollment, New York Heart Associate (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities * Uncontrolled hypertension or diabetes * Acute active infection requiring systemic antibiotics, antivirals, or anti fungals within two weeks prior to first dose * Known or suspected human immunodeficiency (HIV) infection, known HIV seropositivity * Active hepatitis A, B, or C infection * Non-hematologic malignancy within the past 3 years except adequately treated basal cell, squamous cell skin cancer, thyroid cancer, carcinoma in situ of the cervix or breast, prostate cancer \< Gleason grade 6 with stable prostate specific antigen levels or cancer considered cured by surgical resection alone * Any clinically significant medical disease or condition that, in the investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent * Significant neuropathy (grades 3-4, or grade 2 with pain) at the time of the first dose and/or within 14 days before enrollment * Contraindications to any of the required concomitant drugs, including proton-pump inhibitor (eg, lansoprazole), enteric-coated aspirin, allopurinol or if a history of prior thrombotic disease, warfarin or low molecular weight heparin * Subjects in whom the required program of PO and IV fluid hydration is contraindicated, eg, due to pre-existing pulmonary, cardiac, or renal impairment * Subjects with known or suspected amyloidosis of any organ * Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis * Prior exposure to daratumumab