• 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