Inclusion Criteria:
* Men or women ≥ 18 and ≤ 80 years old
* Diagnosis of multiple myeloma:
* Serum monoclonal protein ≥ 0.5 g/dL. Patients with IgD disease and lower amounts of monoclonal protein may be permitted to enroll with PI approval
* ≥ 200 mg of monoclonal protein in the urine on 24 hour electrophoresis
* Serum free light chain ≥ 100 mg/L (10 mg/dL) and abnormal serum free kappa to serum free kappa light chain ratio
* Previously treated relapsed and refractory multiple myeloma
* Patients must have received at least one prior line of therapy;
* Prior therapy must include at least 2 cycles of lenalidomide and at least 2 cycles of a proteasome inhibitor (either in separate regimens or within the same regimen)
* Disease progression on or within 60 days of completion of last therapy.
* ANC ≥ 1000/μL.
* G-CSF is not permitted within 14 days of screening.
* Patients with ANC \<1000/µL can be considered for screening on a case by case basis with additional monitoring, after discussion with and approval from the PI.
* Platelet count ≥ 50,000/µL. Platelet transfusion is not permitted within 7 days of screening.
* Hemoglobin ≥ 8 g/dL. Red blood cell transfusions are permitted to meet eligibility criteria.
* Calculated creatinine clearance of ≥ 30 mL/min by Cockcroft-Gault equation.
* Patient has adequate hepatic function, as evidenced by each of the following:
* Serum bilirubin values \< 2 mg/dL; and
* Serum aspartate transaminase (ALT) and/or aspartate transaminase (AST) values \< 2.5 × the upper limit of normal (ULN) of the institutional laboratory reference range. Patients with elevated bilirubin due to Gilbert's syndrome may be permitted with PI approval (e.g. total bilirubin \<3 mg/dL and normal direct bilirubin).
* Must be able to take acetylsalicylic acid (ASA) daily as prophylactic anticoagulation. Patients intolerant to ASA may use low molecular weight heparin, apixaban, rivaroxaban, or equivalent.
* All study participants must be registered into the mandatory Pomalyst REMS program and be willing and able to comply with the requirements of the Pomalyst REMS program.
* Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Pomalyst REMS program.
* A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control e.g. either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 3 months after receiving the last dose of study drug.
* Able to swallow capsules whole (pomalidomide capsules cannot be crushed, dissolved or broken).
Exclusion Criteria:
* Participants who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to study registration or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier. Patients may have received dexamethasone within 2 weeks prior to study registration.
* Participants who are receiving any other investigational agents.
* Last line of therapy with the combination of carfilzomib, pomalidomide, and dexamethasone. Note, prior treatment with daratumumab or other anti-CD38 therapy is permitted. Prior treatment with carfilzomib or pomalidomide is permitted (as different lines of treatment but not in the same combination).
* Concomitant high dose corticosteroids. Low dose corticosteroids (maximum dose 10 mg/day prednisone equivalent) is permitted if given for disorders other than myeloma, e.g. adrenal insufficiency, rheumatoid arthritis, etc.
* Pregnancy or lactation or planned lactation (breastfeeding).
* Prior history of malignancies, other than MM, unless the patient has completed definitive treatment and has been free of the disease for ≥ 3 years. Patients who are free of disease \< 3 years may enroll after discussion with and approval of the PI. Exceptions include the following (i.e. the following are eligible to participate):
* Basal or squamous cell carcinoma of the skin
* Carcinoma in situ of the cervix
* Ductal carcinoma in situ of the breast
* Incidental histologic finding of prostate cancer (T1a or T1b) managed with surveillance
* Patients with plasma cell leukemia, POEMS syndrome, or amyloidosis are excluded from this trial.
* Seropositive for HIV infection
* Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]; see exception below). Subjects with resolved infection (ie, subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. Exception: subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR.
* Seropositive for hepatitis C (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy).
* Peripheral neuropathy ≥ grade 2 despite supportive therapy.
* Hypersensitivity to daratumumab, thalidomide, lenalidomide, pomalidomide, carfilzomib, or dexamethasone (such as Stevens-Johnson syndrome). Rash to immunomodulatory drug that can be medically managed is allowable.
* Allogeneic stem cell transplant \<12 months prior to initiation of study treatment and who have not discontinued immunosuppressive treatment for at least four weeks prior to initiation of study treatment and who are currently dependent on such treatment. Patients may also not have active graft v. host disease (GVHD).
* Patient has a history of significant cardiovascular, neurological, endocrine, gastrointestinal, respiratory, or inflammatory illness that could preclude study participation, pose an undue medical hazard, or interfere with the interpretation of the study results, including, but not limited to, patients with congestive heart failure (New York Heart Association \[NYHA\] Class 3 or 4); unstable angina; cardiac arrhythmia; recent (within the preceding 6 months) myocardial infarction or stroke; hypertension requiring \> 2 medications for adequate control; diabetes mellitus with \> 2 episodes of ketoacidosis in the preceding 12 months; or chronic obstructive pulmonary disease (COPD) requiring \> 2 hospitalizations in the preceding 12 months.
* Known chronic obstructive pulmonary disease (COPD) (defined as a forced expiratory volume \[FEV\] in 1 second \<60% of predicted normal), known moderate or severe persistent asthma within 2 years prior to study registration (intermittent asthma is allowed). Patient with known or suspected COPD or asthma must have an FEV1 test within 28 days prior to study registration.
* Major surgery within 2 weeks prior to C1D1.
* Patient has any other medical, psychiatric, or social condition that would preclude participation in the study, pose an undue medical hazard, interfere with the conduct of the study, or interfere with interpretation of the study results.
* Toxicity from previous anticancer therapy must resolve to baseline levels or to grade ≤1, except for alopecia and peripheral neuropathy.
