Pomalidomide, Dexamethasone, and Filgrastim-sndz in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Relapsed and/or refractory multiple myeloma with measurable disease, as defined by one or both of the following (assessed within 14 days prior to initiation of therapy): a) serum myeloma protein (M-protein) \>= 0.5 g/d; b) urine Bence-Jones protein \>= 200 mg/24 hours * Patients with light chain only myeloma are eligible; the involved free light chain level \>= 100 mg/L with abnormal serum free light chain ratio * Patients must have prior treatment with \>= 2 cycles of lenalidomide and \>= 2 cycles of bortezomib (either in separate regimens or as part of the same regimen) (primary refractory of subjects refractory to the most recent regimen are eligible) * The patient has received =\< 5 lines of prior therapy * Eastern Cooperative Oncology Group performance status 0 - 2 * Serum alanine aminotransferase (ALT) \< 3.5 times the upper limit of normal within 7 days of time of consent * Serum direct bilirubin \< 2 mg/dL (34 Omol/L) within 7 days of time of consent * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L within 7 days of time of consent, without granulocyte- colony stimulating factor (G-CSF) * Hemoglobin \> 9 g/dL (80 g/L) within 7 days of time of consent (subjects may be receiving red blood cell transfusions in accordance with institutional guidelines) * Platelet count \> 100 x 10\^9/L * Creatinine clearance \> 50 mL/minute within 7 days of time of consent, either measured or calculated using a standard formula (e.g., Cockcroft and Gault) * Written informed consent in accordance with federal, local, and institutional guidelines * All study participants must be registered into the mandatory POMALYST (pomalidomide) Risk Evaluation and Mitigation Strategy (REMS) program, and be willing and able to comply with the requirements of the POMALYST REMS program * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days and again within 24 hours prior to starting cycle 1 of pomalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking pomalidomide; FCBP must also agree to ongoing pregnancy testing and follow pregnancy testing requirements as outlined in the POMALYST REMS program; men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy; all patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure Exclusion Criteria: * Hypersensitivity to previous lenalidomide or thalidomide * History of serious allergic reactions to pegfilgrastim or filgrastim * Chemotherapy (approved or investigational) within 3 weeks prior to signing consent * Antibody therapy within 6 weeks prior to signing consent * Radiotherapy to \>= 3 sites at the same time within 1 week prior to signing consent * Immunotherapy within 28 days prior to signing consent * Pregnant or breast feeding females * Major surgery within 21 days prior to signing consent * Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to signing consent * Known human immunodeficiency virus infection * Known active hepatitis B or C infection * Unstable angina or myocardial infarction within 4 months prior to registration, 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 * Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to signing consent * Non-hematologic 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 * Significant neuropathy (grades 3 - 4, or grade 2 with pain) within 14 days prior to signing consent * Subjects with known or likely systemic amyloidosis * Ongoing graft-vs-host disease * 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