Carfilzomib, Pegylated Liposomal Doxorubicin Hydrochloride, and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Histologically confirmed diagnosis of multiple myeloma with a measurable disease parameter at time of screening; a measurable disease parameter is defined as one or more of the following: * Serum monoclonal protein \>= 0.5 g/dl * 24 hour urine monoclonal protein \>= 0.2 g/24 hour * Serum free light chain ratio \> 5 x normal ratio with an absolute difference of 10mg/dl between the involved and uninvolved free light chain * Soft tissue plasmacytoma \>= 2 cm measurable by either physical examination and/or applicable radiographs (e.g. magnetic resonance imaging \[MRI\], computed tomography \[CT\], etc) * Bone Marrow Plasma Cells \>= 30% * Documentation of at least one line of prior myeloma therapy now with relapsed or refractory disease requiring re-treatment * At least 18 years of age at the time of signing the informed consent. * Performance status of Eastern Cooperative Oncology Group (ECOG) =\< 2 or Karnofsky \>= 60%; participants with lower performance status based solely on bone pain secondary to multiple myeloma will be eligible * Required laboratory values * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) and aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) \< 2.5 x the upper limit of the institutional normal value (ULN) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Absolute neutrophil count (ANC) \>= 1,000 * Hemoglobin \>= 8 g/dl * Platelets \>= 50,000 * Creatinine clearance \> 15 ml/minute using Cockcroft-Gault formula * For those participants receiving warfarin (Coumadin), unfractionated heparin, or low-molecular weight heparin therapy, the applicable coagulation parameter that is being monitored must be within the accepted therapeutic ranges for those indications * Transfusions and/or growth factor dependent participants are not excluded if the above parameters can be achieved with such support * Females of childbearing potential (FCBP) must agree to refrain from becoming pregnant while on study drug and for 3 months after discontinuation from study drug, and must agree to use adequate contraception including hormonal contraception, (i.e. birth control pills, etc), barrier method contraception (i.e. condoms), or abstinence during that time frame; FCBP must agree to regular pregnancy testing during this timeframe; inclusion of FCBP requires two negative pregnancy tests prior to enrollment. All women, regardless of age, should be considered FCBP unless they are surgically sterile (post hysterectomy, post bilateral oophorectomy, etc) or have been naturally post menopausal for \>= 24 consecutive months * Men engaging in sexual intercourse with a FCBP must agree to use adequate contraception including hormonal contraception, (i.e. birth control pills, etc), barrier method contraception (i.e. condoms), or abstinence while on study drug and for 3 months after discontinuation from study drug * Ability to understand and willing to sign a written informed consent document Exclusion Criteria: * POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Plasma Cell Leukemia * Waldenstrom's macroglobulinemia * Pregnant or lactating females * Use of any anti-myeloma drug therapy within 14 days of initiation of study drug treatment excluding corticosteroids if given for an indication other than myeloma; bisphosphonates are not considered anti-myeloma drugs * Participation in an investigational therapeutic study within 14 days of initiation of study drug treatment * Radiotherapy to multiple sites or immunotherapy within 14 days of initiation of study drug treatment (localized radiotherapy to a single site at least 7 days before start is permissible) * Major surgery within 14 days of initiation of study drug treatment * Participants in whom the required program of oral (PO) and IV fluid hydration is contraindicated * Prior history of a hypersensitivity reaction to PLD, doxorubicin, bortezomib, carfilzomib, or liposomal drug formulations other than PLD; history of reactions to liposomal drug formulations other than PLD should be evaluated individually and if their reactions were felt to have been due to the encapsulated agent, rather than the liposomal component itself they should be excluded at the discretion of the investigators * Participants who are known to have active hepatitis A, B, or C viral infection may not participate in this study; active disease is defined as participants with a known viral hepatitis whose liver function tests are elevated * Known human immunodeficiency virus (HIV)-seropositive and are taking anti-retrovirals may not participate in this study; participants who are HIV-seropositive and not on anti-retroviral therapy and who otherwise meet the inclusion/exclusion criteria will be eligible for the study * Compromised cardiovascular function defined as any of the following: * Electrocardiogram (EKG) evidence of acute ischemia * EKG evidence of medically significant conduction system abnormalities * History of myocardial infarction within the last 6 months * Unstable angina pectoris or cardiac arrhythmia * History of Class 3 or Class 4 New York Heart Association Congestive Heart Failure within 6 months of enrollment on study * Left ventricular ejection fraction (LVEF) \< 45% by either echocardiography or radionuclide-based multiple gated acquisition (Echo or MUGA) * Uncontrolled concurrent illness including: other hematologic or non-hematologic malignancy, active infection, or uncontrolled diabetes * Any significant psychological, medical, or surgical condition thought to compromise the participant, the study, or prevent informed consent