S1304, Carfilzomib and Dexamethasone for Treating Patients With Relapsed or Refractory Myeloma

Inclusion Criteria: * REGISTRATION STEP 1: INITIAL RANDOMIZATION * Patients must have a confirmed diagnosis of symptomatic multiple myeloma and must be currently relapsed or refractory; all tests for establishing disease status must be completed within 28 days prior to registration and documented on the Baseline Tumor Assessment Form for Multiple Myeloma * Patients must have measurable disease within 28 days prior to registration * Patients must have received at least one prior regimen of chemotherapy for symptomatic multiple myeloma; patients may not have more than six (6) previous regimens of therapy for the disease; prior chemotherapy must have been completed at least 21 days prior to registration; for study purposes, a regimen is defined as follows: * An anti-myeloma therapy used at the time of initial diagnosis or documented disease progression which is given with the intent to decrease disease burden * Any maintenance therapy used after an Induction should be considered part of that Induction regimen * Use of any agent or combination of agents more than once during the patient's disease history for separate documented disease progressions will be counted as separate regimens (e.g., if a patient receives lenalidomide/bortezomib at initial diagnosis and achieves response, but then progresses and receives lenalidomide/bortezomib after progression, these count as 2 separate regimens) * In cases of allogeneic or autologous stem cell transplant, the entire induction + stem cell mobilization + conditioning + planned maintenance should be considered one regimen * Patients may not have received any prior carfilzomib treatment * Patients must not be receiving any other concurrent therapy considered to be investigational; patients must not be planning to receive any radiotherapy (except localized radiation for palliative care); patients must not be planning to receive any concurrent chemotherapy, immunotherapy, radiotherapy or other treatment with curative intent * Patients must have complete history and physical examination within 28 days prior to registration * Patients must have baseline PET scan within 28 days prior to registration; note that images are submitted centrally for review * Patients with non-secretory MM or known primary amyloidosis are not eligible * Patients must have Zubrod performance status 0-2 * Patients must not have clinically significant illness including uncontrolled, active infection requiring intravenous antibiotics, New York Heart Association (NYHA) class III or class IV heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, or \>= grade 3 cardiac arrhythmias * Patients must have undergone an electrocardiogram (EKG) within 28 days prior to registration * Patients must have either echocardiogram (ECHO) with ejection fraction \>= 45% within 28 days prior to registration * Patients must not have \> grade 2 neuropathy and/or POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) =\< 3 x ULN * Absolute neutrophil count (ANC) \>= 1,000 cell/mm\^3 without growth factor support within 14 days prior to registration * Platelets \>= 50,000 cells/mm\^3 for patients who have bone marrow plasmacytosis \< 50% or \>= 30,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \>= 50% within 14 days prior to registration * Calculated or measured creatinine clearance \>= 30 ml/min within 14 days prior to registration * Patients who are known to be human immunodeficiency virus positive (HIV+) are eligible providing they meet all of the following additional criteria within 28 days prior to registration: * Cluster of differentiation (CD)4 cells \>= 500/mm\^3 * Viral load of \< 50 copies HIV messenger ribonucleic acid (mRNA)/mm\^3 if on combination antiretroviral therapy (cART) or \< 25,000 copies HIV mRNA if not on cART * No zidovudine or stavudine as part of cART * Patients who are HIV+ and do not meet all of these criteria are not eligible for this study * Patients with known hepatitis B or hepatitis C infection must have viral load \< 800,000 IU/L within 28 days prior to registration * Patients must have baseline skeletal survey to document lytic lesions, osteopenia or compression fracture within 28 days prior to registration * Patients may have received palliative external beam radiation therapy (XRT) for local disease control with no curative intent. XRT must be completed at least 7 days prior to registration * Patients must be offered participation in specimen submission for translational medicine studies and banking; with patient consent, specimens must be submitted * Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for three years * Patients or their legally authorized representative must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * REGISTRATION STEP 2: CROSSOVER * Patient must have been eligible for and initially randomized to Arm 1 (low dose carfilzomib), begun cycle 2 of treatment, and progressed prior to completing 12 cycles of protocol therapy * At least 14 days and no more than 28 days must have elapsed between the last day of treatment on Arm 1 and registration to Arm 3 * Patients must have recovered from all non-hematologic toxicities to =\< grade 2 and from all hematologic toxicities to =\< grade 3 prior to registration * Patients must have begun cycle 2 (carfilzomib - 27 mg/m\^2) and must not have received any dose reduction for toxicity in the last cycle of treatment, immediately preceding progression * Patients must have serum protein electrophoresis (SPEP) and kappa and lambda light chain testing performed within 14 days prior to registration in order to establish baseline measurements * Patients must not have ejection fraction decrease \> 10% from baseline (as determined by ECHO) or other ejection fraction decrease accompanied by other clinical signs/symptoms of New York Heart Association (NYHA) class III or IV heart failure, measured within 28 days prior to registration; if any question exists regarding individual patient eligibility in this situation, contact the study chair for determination