Carfilzomib in Treating Patients With Multiple Myeloma in First Relapse or Refractory to First-Line Therapy

Inclusion Criteria:

* Multiple myeloma (MM) in first relapse or refractory to first line therapy; the previous line of therapy should include either an immunomodulatory agent or a proteasome inhibitor

  * Refractory disease is defined as =\< 25% response or progression during therapy or within 60 days after completion
  * The number of prior lines of anti-myeloma therapy will be determined as follows:

    * Induction chemotherapy for peripheral-blood stem cell harvest followed by planned mobilization and subsequent high-dose chemotherapy with autologous stem cell transplant (ASCT) is considered one therapy regardless of the induction regimen
    * Planned maintenance therapy after stem cell transplantation or other induction therapy is not considered a separate line of therapy, as long as there is no evidence of progression in the time between the induction or transplantation and the initiation of maintenance therapy
    * Two ASCTs within 6 months of each other is considered as one line unless different agents were used in the high-dose therapy-conditioning regimens
    * If the same regimen is repeated after a 6-month interval, they are considered to be two separate therapeutic lines
    * If cyclophosphamide is used for reasons other than planned stem cell mobilization, its use is considered to be a separate line of therapy
    * Dose modification of steroid and altering choices of steroid (i.e. from dexamethasone to prednisone) due to side effects, is not considered a line of therapy, as long as there is no evidence of progression
    * If a regimen was stopped for more than 2 months, its re-initiation is counted as another line of therapy
* Presence of existing lytic bone lesions either by skeletal X-ray, computed tomography (CT) scan or magnetic resonance imaging (MRI) scan
* Measurable MM disease, defined as one of the following:

  * A monoclonal immunoglobulin (Ig) concentration on serum electrophoresis of \>= 0.5 g/dL for an IgG myeloma, \>= 0.1 g/dL for an IgD myeloma or \>= 0.5 g/dL for an IgA myeloma
  * Measurable urinary light chain secretion by quantitative analysis of \>= 200 mg/24 hours
  * Involved serum free light chain (FLC) level \>= 10 mg/dL, provided the serum FLC ratio is abnormal
  * Patients with oligo- or non-secretory disease must have bone marrow involvement with at least 30% plasmacytosis on aspiration
* Life expectancy \>= 3 months as determined by the treating physician
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0, 1 or 2
* Absolute neutrophil count (ANC) \>= 1.0 × 10\^9/L (without transfusion support and without hematological growth factor support within 2 weeks of cycle 1 day 1)
* Platelets \>= 50 × 10\^9/L; if the bone marrow contains \>= 50% plasma cells, a platelet count of \>= 30 × 10\^9/L is allowed (without transfusion support and without hematological growth factor support within 2 weeks of cycle 1 day 1)
* Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and/or alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) =\< 2.5 × the upper limit of normal (ULN)
* Bilirubin \< 2.0 mg/dL
* Serum creatinine =\< 3.0 mg/dL or a calculated creatinine clearance of at least 15 mL/min (using the Cockcroft and Gault method)
* Adequate cardiac function defined as left ventricular ejection fraction (LVEF) \>= 40%

  * NOTE: 2-dimensional (2-D) transthoracic echocardiogram (ECHO) is the preferred method of evaluation
  * Multigated acquisition scan (MUGA) is acceptable if ECHO is not available
* Written informed consent in accordance with federal, local, and institutional guidelines
* Females of childbearing potential (FCBP) must agree to ongoing pregnancy testing and to practice contraception; females are considered of childbearing potential unless they are surgically sterile (they have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months
* Male subjects must agree to practice contraception

Exclusion Criteria:

* No primary amyloidosis
* No plasma cell leukemia (\> 2.0 × 10\^9/L circulating plasma cells by standard differential)
* No treatment with an investigational product or device within 21 days of cycle 1 day 1
* No history of allergic reaction/hypersensitivity to any of the study medications, their analogues or excipients in the various formulations
* No treatment with cytotoxic therapy or monoclonal antibodies within 21 days prior to cycle 1 day 1
* No treatment with a steroid intended to treat myeloma within 14 days prior to cycle 1 day 1
* No autologous or allogeneic stem cell transplant within 3 months prior to cycle 1 day 1
* No radiotherapy within 21 days prior to cycle 1 day 1; however, if the radiation portal covered =\< 5% of the bone marrow reserve, the patient may be enrolled irrespective of the end date of radiotherapy
* No major surgery within 14 days and minor surgery within 7 days prior to cycle 1 day 1
* No pregnant or lactating females
* No acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to cycle 1 day 1
* No known human immunodeficiency virus (HIV) infection
* No active hepatitis B or C infection
* No unstable angina or myocardial infarction within 4 months prior to cycle 1 day 1, New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or grade 3 conduction system abnormalities unless subject has a pacemaker
* No uncontrolled hypertension or uncontrolled diabetes (as determined by the treating physician) within 14 days prior to cycle 1 day 1
* No nonhematologic malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas
* No significant neuropathy (grades 3-4, or grade 2 with pain) within 14 days prior to cycle 1 day 1
* No known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib)
* No 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
* No subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to cycle 1 day 1
* Any other 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