Selinexor, Pomalidomide, and Dexamethasone With or Without Carfilzomib for the Treatment of Patients With Relapsed Refractory Multiple Myeloma, The SCOPE Trial

Inclusion Criteria: * Age \>= 18 years * Diagnosis of RRMM with progressive disease at study entry as per the International Myeloma Working Group (IMWG) uniform criteria * Measurable disease by IMWG criteria as defined by at least one of the following: * Serum M-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg in a 24-hour collection * Serum free light chain level \>= 10 mg/dL provided the free light chain ratio is abnormal * For patients with extramedullary measurable disease (EMD) by CT or MRI or the CT portion of the PET/CT: Must have at least one lesion that has a single diameter of \>= 2 cm. Skin lesions can be used if the area is \>= 2cm in at least one diameter and measured with a ruler * Bone marrow plasma cells \>= 30% * Patients with IgA myeloma in whom serum protein electrophoresis is deemed unreliable, due to co-migration of normal serum proteins with the para protein in the beta region, may be considered eligible as long as total serum IgA level is elevated above normal range * Prior treatment: * Arm A: At least one of the following must be true: (1) Subjects must have been previously treated with at least 3 prior lines of therapy, including a proteasome inhibitor and an immunomodulatory drug (IMiD) (2) Subjects who are refractory to carfilzomib and/or pomalidomide may enroll in Arm A using the quadruplet regimen, SKPd, provided carfilzomib, pomalidomide and dexamethasone (KPd) triplet is not the most recent line of prior therapy and that they have been previously treated with at least 3 prior lines of therapy, including a proteasome inhibitor and an IMiD. Carfilzomib/Pomalidomide refractory status is defined by the IMWG criteria: disease that is nonresponsive (stable disease \[SD\] or progressive disease \[PD\]) while on therapy, or progresses within 60 days of last therapy in patients who have achieved minimal response (MR) or better at some point previously before then progressing in their disease course. * Arm B: Subjects must have progressive disease and been exposed to up to 2 prior lines of therapy, including a proteasome inhibitor and lenalidomide * Provide written informed consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) and ability to adhere with the study visit schedule and other protocol procedures * Willingness to provide mandatory tissue specimens for correlative research * Willingness to use fixed-duration therapy (up to 18 cycles) for relapsed refractory multiple myeloma * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Ability to complete questionnaire(s) by themselves or with assistance * Willingness to provide mandatory blood specimens for correlative research * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 15 mL/min (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/uL(without growth factor support for \>= 7 days ( obtained =\< 14 days prior to registration) * Un-transfused Platelet count \>= 100,000/uL (without platelet transfusion for \>= 14 days) for SKPd and \>= 100,000 (without platelet transfusion for \>= 7 days) for SPd is permitted. Additionally, for both Arms A and B platelet count of \>= 75,000/uL is permitted if thrombocytopenia is deemed by the investigator to be secondary to severe bone marrow infiltration (\>= 50%) by myeloma as determined * Hemoglobin \>= 8.0 g/dL Note: Screening hemoglobin should be independent of red blood cell transfusion for at least 3 days prior to screening * Total bilirubin =\< 2.0 x upper limit of normal (ULN). Note: Patients with Gilbert's syndrome who must have a total bilirubin of \< 3 times ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN * Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN * Note: If patient is receiving warfarin and INR should be within 2-3 * Negative serum pregnancy test done =\<7 days prior to registration, for persons of childbearing potential only * Willingness to follow strict birth control measures as suggested by the study: Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for 28 days prior to starting pomalidomide, during the course of the study, during any dose interruptions, and through 30 days after last dose of pomalidomide and carfilzomib. Female subjects of child bearing potential are those who 1) have achieved menarche at some point, 2) have not undergone a hysterectomy or bilateral oophorectomy or 3) have not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Male subjects must agree to practice abstinence or use an effective barrier method of contraception starting with the first dose of carfilzomib or pomalidomide through 6 months after last dose of pomalidomide and carfilzomib if sexually active with a female of childbearing potential. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Other acceptable methods of contraception are condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal. All subjects must agree to follow the local requirements for pomalidomide counseling, pregnancy testing, and birth control; and be willing and able to comply with the local requirements (for example, periodic pregnancy tests, safety labs, etc.) * Willingness to follow the requirements of the Pomalyst Risk Evaluation and Mitigation Strategy (REMS) program * Able to swallow capsules and able to take and tolerate oral medications on a continuous basis Exclusion Criteria: * History of myocardial infarction =\< 6 months prior to pre-registration, or congestive heart failure requiring use of ongoing maintenance therapy for life threatening ventricular arrhythmias. Unstable angina within 4 months prior to randomization, New York Heart Association (NYHA) class III or IV heart failure, left ventricular ejection fraction (LVEF) \< 40%, uncontrolled angina, corrected QT (QTc) interval \>= 470 msec, History of severe coronary artery disease, severe uncontrolled ventricular arrhythmias including uncontrolled chronic atrial fibrillation/atrial flutter, history of torsades de pointe, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or grade 3 conduction system abnormalities unless subject has a pacemaker * Failure to recover from acute, reversible effects of prior therapy regardless of interval since last treatment. EXCEPTION: Grade 1 peripheral (sensory) neuropathy that has been stable for at least 1 month since completion of prior treatment * Uncontrolled intercurrent non-cardiac illness including, but not limited to: * Ongoing or active infection. Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals =\< 14 days prior to registration; patients with controlled infection or on prophylactic antibiotics are permitted in the study * Psychiatric illness/social situations * Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy * Any other conditions that would limit compliance with study requirements * Patients known to be human immunodeficiency virus (HIV) positive and/or currently receiving antiretroviral therapy * Currently receiving any other investigational agent which would be considered as a treatment for RRMM * Non investigational radiation, chemotherapy, or immunotherapy or any other anticancer therapy =\< 14 days or five half-lives, whichever is shorter prior to registration. Note: (localized radiation to a single site =\< 7 days prior to registration is allowed) * Participation in an investigational anti-cancer study =\< 21 days or five half-lives whichever is shorter prior to registration * Major Surgery =\< 21 days prior to registration * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Other active malignancy =\< 5 years prior to registration. EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix that has undergone potentially curative therapy. NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer * Uncontrolled hypertension or uncontrolled diabetes =\< 14 days prior to registration * Known active hepatitis A, B, or C infection; or known to be positive for hepatitis C virus (HCV) ribonucleic acid (RNA) or hepatitis B surface antigen (HBsAg) \[hepatitis B virus (HBV) surface antigen\] * Significant neuropathy (grades 3-4, or grade 2 with pain) =\< 14 days prior to registration * Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) * Any underlying condition that would significantly interfere with the absorption of an oral medication * Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment * Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis =\< 14 days prior to registration * Patients with coagulation problems and active bleeding in the last month (e.g, peptic ulcer, epistaxis, spontaneous bleeding) * Subjects with smoldering multiple myeloma (SMM), monoclonal gammopathy of undetermined significance (MGUS) or Waldenström's macroglobulinemia or AL amyloidosis * History of repeated infections, hyperviscosity or POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Has a known history of immunosuppression or is receiving systemic steroid therapy or any other form of systemic immunosuppressive therapy =\< 7 days prior registration. The use of physiologic doses of corticosteroids may be approved after consultation with the study chair * Note: A short course of 40 mg dexamethasone (=\< 4 days) or equivalent for emergency use is allowed after previous consultation with the study chair. In these cases, baseline m-protein values from serum and urine should be obtained before the short steroid course and be repeated prior to study drugs administration on cycle 1 day 1 * Treatment with plasmapheresis =\< 28 days prior to registration * Known hypersensitivity to thalidomide, lenalidomide or dexamethasone * Unable or unwilling to undergo thromboembolic prophylaxis including, as clinically indicated, aspirin, Coumadin (warfarin) or low-molecular weight heparin * Evidence of active, non-infectious pneumonitis * Received a live vaccine =\< 30 days prior to registration * Pomalidomide and carfilzomib (for arm A) or pomalidomide (for Arm B) commercially unavailable to the patient * Prior exposure to Selinexor * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception (applies to both male and female participants as written)