A Phase I/II Trial of Carfilzomib, Pegylated Liposomal Doxorubicin, and Dexamethasone for the Treatment of Relapsed/Refractory Multiple Myeloma

• 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