Personalized Autologous Transplant for Multiple Myeloma

Inclusion Criteria: * Patient must have the clinical diagnosis of a plasma cell neoplasm requiring treatment per the treating physician using the International Myeloma Working Group (IMWG) and World Health Organization (WHO) criteria as guidelines. This can include extraosseous plasmacytoma, monoclonal immunoglobulin deposition disease, and heavy-chain diseases as these diagnoses, while rare, can be treated in part with autologous transplant * If enrolling in phase A of this protocol, the patient * must have received 2+ lines of therapy as defined by the IMWG; and * Must have estimated glomerular filtration rate (eGFR) by Cockcroft-Gault \> 40 mL/min; and * Be eligible and appropriate per the treating physician to receive 200 mg/m\^2 * If enrolling in phase B of the protocol, the transplant must be part of first line therapy to provide some level of homogeneity for toxicity assessment and preliminary efficacy * Absolute neutrophil count (ANC) \>= 1000/uL * Platelet count \>= 100,000 * Total bilirubin \< 1.5 x institutional upper limit of normal (unless the patient has an established diagnosis of Gilbert's in which case total bilirubin \< 3 mg/dL) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 3 x the institutional upper limit of normal * Left ventricular ejection fraction \>= 45% * Diffusion capacity of the lung for carbon monoxide (DLCO), forced expiratory volume in 1 second (FEV1), and forced vital capacity (FVC) \> 50% of predicted value (corrected for hemoglobin) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) is required for eligibility. Those patients with lower performance status based solely on bone pain secondary to multiple myeloma are eligible * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test prior to starting therapy. The effects of protocol therapy on the developing human fetus are unknown. For this reason, FCBP and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of protocol therapy administration. Female of childbearing potential (FCBP) is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * The patient must be willing to comply with fertility requirements * Ability to understand and the willingness to sign a written informed consent document * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial Exclusion Criteria: * Patients known to meet criteria for progressive disease or clinical relapse between screening and planned melphalan infusion day -3 * Subject has any of the following cardiac abnormalities * History of clinically significant cardiovascular disease with New York Heart Association class III or IV congestive heart failure or * Severe non-ischemic cardiomyopathy or * Myocardial infarction within the previous 6 months prior to starting study treatment * Unstable or poorly controlled angina * Uncontrolled severe hypertension * Clinically/hemodynamically significant arrythmias * Severe uncontrolled cardiac arrhythmias (grade 3 or higher) or * Clinically significant electrocardiogram (ECG) abnormalities includingcorrected QT interval (QTc) \> 480 msec * Human immunodeficiency virus (HIV) positive EXCEPT if the patient meets all the following: CD4 \> 350 cells/mm\^3, undetectable viral load, maintained on modern therapeutic regimen utilizing non CYP interacting agents (e.g. excluding ritonavir), and no untreated acquired immune deficiency syndrome defining opportunistic infections. * Seropositive for hepatitis B surface antigen \[HBsAg\]) EXCEPT subjects with resolved infection (ie, subjects who are positive for antibodies to hepatitis B core antigen \[antiHBc\] and/or antibodies to hepatitis B surface antigen \[antiHBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. Subjects with serologic findings suggestive of HBV vaccination (antiHBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR * Seropositive for hepatitis C except in the setting of a sustained virologic response \[SVR\], defined as without viremia for at least 12 weeks after completion of antiviral therapy * Polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin change (POEMS) syndrome, amyloid light-chain (AL) amyloidosis, and Waldenstrom macroglobulinemia * Concurrent medical condition or disease (eg, active systemic infection) that is likely to interfere with study procedures or results, or that in the opinion of the investigator would constitute a hazard for participating in this study * Known or suspected of not being able to comply with the study protocol (eg, because of alcoholism, drug dependency, or psychological disorder) or the subject has any condition for which, in the opinion of the investigator, participation would not be in the best interest of the subject (eg, compromise their well-being) or that could prevent, limit, or confound the protocol-specified assessments * Pregnant women are excluded from this study because protocol therapy has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to protocol treatment of the mother, breastfeeding should be discontinued