Selinexor, Daratumumab, Carfilzomib and Dexamethasone for the Treatment of High-Risk, Recurrent or Refractory Multiple Myeloma

Inclusion Criteria:

* Age \>= 18 years
* Patients must have a documented history of relapsed or relapsed/refractory MM as defined by International Myeloma Working Group (IMWG) criteria (Rajkumar et al., 2014)

  * Patients must be selinexor and carfilzomib sensitive
  * Prior daratumumab exposure is allowed, provided that it has been 6 months or more from the time of cycle 1 day 1 (C1D1) of protocol therapy
* High risk disease defined as 1 or more of the following:

  * High risk cytogenetics (any of the following)

    * t(4;14), t(14;16), t(14;20)
    * del(17p)
    * del(1p)
    * Gain 1q (\>= 3 copies)
  * Lactate dehydrogenase (LDH) \> upper limit of normal at relapse
  * International Staging System (ISS) stage 3 disease at relapse
  * Extramedullary disease at diagnosis or relapse
  * \>= 5% circulating plasma cells at diagnosis or relapse
  * High risk by gene expression profiling, if known, at diagnosis or relapse
  * Early relapse with first-line therapy

    * =\< 18 months from cycle 1 day 1 for patients not undergoing autologous stem cell transplant (ASCT)
    * =\< 36 months from cycle 1 day 1 for patients undergoing ASCT and post-ASCT maintenance
* Measurable disease
* 1-3 prior lines of therapy
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 2 (Form is available on the Academic and Community Cancer Research United \[ACCRU\] website)
* Patients must have evidence of adequate bone marrow reserves, as defined by the following:

  * Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3 without filgrastim or its equivalent within 1 week of the initiation of treatment or pegfilgrastim or its equivalent within 2 weeks of the initiation of treatment
  * Platelet count of \>= 100,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \< 50%, or \>= 50,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \> 50%, both without platelet transfusion support within 1 week of the initiation of treatment or the use of TPO mimetics
  * NOTE: If your site laboratory reports use different units of measurements than what is required by the protocol eligibility requirements, please use the "Lab Test Unit Conversion Worksheet" available on the ACCRU website under "General Forms"
* Total bilirubin =\< 2.0 times the upper limit of the institutional normal values except in subjects with congenital bilirubinemia, such as Gilbert syndrome (in which case a direct bilirubin =\< 1.5 x upper limit of normal \[ULN\] is required)
* Total aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 times the upper limit of the institutional normal values
* Patients must have adequate cardiac function defined as left ventricular ejection fraction (LVEF) \>= 45% by echocardiogram, magnetic resonance imaging (MRI) or multigated acquisition (MUGA) scan
* For those with symptomatic pulmonary disease (e.g. chronic obstructive pulmonary disease \[COPD\], asthma) or other signs/symptoms of pulmonary disease, adequate pulmonary function as defined by a forced expiratory volume in one second (FEV1) \>= 50% of predicted and diffusing capacity for carbon monoxide (DLCO)/alveolar volume (VA) \>= 50% of predicted within 28 days prior to day 1 of treatment

  * Note: Baseline pulmonary function tests are only required on an as needed basis
* Patients must have evidence of adequate renal function, as defined by the following: creatinine clearance (CrCl) \>= 30 mL/min., as measured by a 24-hour urine collection, or estimated by the Cockcroft and Gault formula

  * Calculated creatinine clearance must be \>= 30 ml/min using the Cockcroft-Gault formula
* Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only
* Female patients of childbearing potential must have a negative serum pregnancy test at screening and agree to use highly effective (dual methods of) contraception throughout the study and for 6 months following the last dose of study drug; and male patients must use an effective barrier method of contraception throughout the study and for 3 months following the last dose of study drug if sexually active
* Ability to complete questionnaire(s) by themselves or with assistance
* Provide informed written consent =\< 28 days prior to registration
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)

Exclusion Criteria:

* Prior treatment with daratumumab within 6 months from cycle 1 day1
* Patient with carfilzomib-refractory disease defined as disease progression on or within 60 days of last carfilzomib dose
* Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects:

  * Pregnant women
  * Nursing women
  * Men or women of childbearing potential who are unwilling to employ adequate contraception
* 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
* Uncontrolled hypertension, defined as a systolic blood pressure of \>= 160 mmHg or a diastolic blood pressure of \>= 90 mmHg
* Significant cardiac disease, including any of the following:

  * \>= class 3 New York Heart Association (NYHA) congestive heart failure
  * Electrocardiogram (EKG) evidence of acute ischemia
  * Unstable angina
  * Myocardial infarction within 6 months prior to day 1 of treatment
  * Clinically significant arrhythmias or conduction block (premature atrial contractions \[PACs\], premature ventricular contractions \[PVCs\], rate controlled atrial fibrillation, sinus arrhythmia, asymptomatic sinus bradycardia or sinus tachycardia and 1st degree heart block are not considered clinically significant)
  * \>= grade 2 QT interval by Fridericia (QTcF) prolongation (i.e. \> 480 ms)
  * Note: Prior to study entry, any EKG abnormality at screening not felt to put the patient at risk must be documented by the investigator as not medically significant
* A diagnosis of human immunodeficiency virus (HIV) does not exclude the patient from participation. However, the viral load must be \< 50 copies/mm\^3 and CD4 count \>= 200 on anti-HIV therapy within 28 days prior to cycle 1, day 1 of treatment
* Positive hepatitis C antibody test result or positive hepatitis C ribonucleic acid (RNA) test result at screening

  * NOTE: Subjects with positive hepatitis C antibody due to prior eradicated disease can be enrolled if a confirmatory negative hepatitis C RNA test is obtained
* Is seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (i.e. 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) deoxyribonucleic acid (DNA) levels. Subjects who are PCR positive will be excluded. Exception: patients with serologic findings suggestive of HBV vaccination
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements
* Discontinuation of prior carfilzomib or daratumumab due to treatment toxicity
* Radiation within 14 days prior to day 1 of treatment. Note: palliative radiation therapy (XRT) to \< 5% of the total marrow volume as assessed by the treating investigator is allowed within 14 days
* Major surgery within 4 weeks prior to day 1 of treatment
* Any multiple myeloma therapy within 14 days prior to cycle 1, day 1
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Active central nervous system (CNS) involvement
* Concomitant amyloid light-chain (AL) amyloidosis or polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes (POEMS) syndrome
* Patients cannot have other prior or concomitant malignancies except for:

  * Non-melanoma skin cancer
  * In situ malignancy
  * Low-risk prostate cancer after curative therapy
  * Prostate cancer Gleason grade 6 AND with stable prostate specific antigen (PSA) levels off treatment
  * Other cancer for which the patient has been treated with curative intent or disease free for \>= 3 years
* Prior exposure to daratumumab within 24 weeks from cycle 1, day 1