Comparing Dara-VCD Chemotherapy Plus Stem Cell Transplant to Dara-VCD Chemotherapy Alone for People Who Have Newly Diagnosed AL Amyloidosis

Inclusion Criteria: * STEP 1: Participants must have systemic AL amyloidosis which is biopsy proven and includes histologically-confirmed by positive Congo red stain with green birefringence on polarized light microscopy, OR characteristic appearance by electron microscopy AND confirmatory AL amyloid typing (mass spectrometry-based proteomic analysis or immunofluorescence). If there is question regarding diagnosis, consult study chairs prior to registration * STEP 1: Participants must have measurable disease within 28 days prior to treatment if initiated prior to registration or within 28 days of registration as defined by at least one of the following: * Positive monoclonal serum immunofixation electrophoresis * Positive monoclonal urine immunofixation electrophoresis * Monoclonal plasma cells in bone marrow In addition, participants must also have a difference between the involved and uninvolved free light chain (dFLC) \>= 2 mg/dL * STEP 1: Participants may receive up to one cycle (or 28 days) of therapy prior to enrollment. If a patient receives \>= 75% of 1 cycle of protocol identical Dara-VCD, this will be considered 1 cycle of protocol induction. Any patient who receives less than 75% of 1 cycle of Dara-VCD or non-protocol therapy will still be eligible but will be treated per protocol. If protocol identical therapy is initiated prior to enrollment, this treatment is not continued but rather treatment is dictated per protocol * STEP 1: Participants may be receiving chronic corticosteroids if they are being given for disorders other than AL amyloidosis or myeloma * STEP 1: Participant must be \>= 18 years old * STEP 1: Participant must have Eastern Cooperative Oncology Group (ECOG) performance score (PS) of 0, 1, or 2 (PS = 3 may be allowed if secondary to neuropathy) * STEP 1: Participant must have a complete medical history and physical exam within 28 DAYS prior to registration * STEP 1: Participants must be willing to undergo high dose chemotherapy and autologous stem cell transplantation if they are randomized to the arm receiving high dose chemotherapy and autologous stem cell transplantation * STEP 1: Participants must be eligible to receive high dose chemotherapy with melphalan at a dose of 200 mg/m\^2 or 140 mg/m\^2 (200 mg/m\^2 is highly encouraged but not mandated). Transplant eligibility criteria are included in the general eligibility criteria listed below: * Participant must have a supine systolic blood pressure (BP) \>= 90 mmHg (at registration step-1, this may by supported by midodrine * Participant must have non-severe cardiac AL (meeting all the below criteria) as defined by: * N-terminal proB-type natriuretic peptide (NT proBNP) \< 5000 (if no NTproBNP, brain natriuretic peptide \[BNP\] must be available and \< 400) * Troponin T (TnT) \< 0.06. If not available, one of the following two criteria must be met: * High sensitivity troponin (hsTnT) T \< 75 or troponin I \< 0.1ng/dL * New York Heart Association (NYHA) I or II * Cardiac ejection fraction (EF) \>= 40% * STEP 1: Hemoglobin \>= 8.0 g/dL (\> 5 mmol/L); red blood cell transfusion allowed up to 7 day prior to registration (within 28 days prior to registration) (NOTE: Growth factor support granulocyte colony-stimulating factor \[G-CSF\] is permitted per institutional guidelines) * STEP 1: Leukocytes \>= 2 x 10\^3/uL (within 28 days prior to registration) (NOTE: Growth factor support \[G-CSF\] is permitted per institutional guidelines) * STEP 1: Absolute neutrophil count \>= 1.0 x 10\^3/uL (within 28 days prior to registration) (NOTE: Growth factor support \[G-CSF\] is permitted per institutional guidelines) * STEP 1: Platelets \>= 50 x 10\^3/uL (within 28 days prior to registration) (NOTE: Growth factor support \[G-CSF\] is permitted per institutional guidelines) * STEP 1: Total bilirubin =\< 1.5 times the institutional upper limit of normal (ULN) unless history of Gilbert's disease. Participants with history of Gilbert's disease must have total bilirubin =\< 5 x institutional ULN (within 28 days prior to registration) * STEP 1: Direct bilirubin =\< 2.0 mg/dL (within 28 days prior to registration) * STEP 1: Aspartate aminotransferase (AST)/ alanine aminotransferase (ALT) =\< 3x upper limit of normal (ULN) (except if secondary to hepatic involvement) (within 28 days prior to registration) * STEP 1: Alkaline phosphatase =\< 750 U/L (except if secondary to hepatic involvement) (within 28 days prior to registration) * STEP 1: Participants must have a serum creatinine =\< the institutional (I)ULN OR measured OR calculated creatinine clearance \>= 30 mL/min using the following Cockcroft-Gault formula. This specimen must have been drawn and processed within 28 days prior to registration * STEP 1: If peripheral neuropathy is present at diagnosis, participants must be grade 2 (moderate symptoms; limiting instrumental activity of daily living \[ADL\]) or less * STEP 1: Participants must have adequate cardiac function. Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants must be class 2 or better * STEP 1: Participants must not be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (i.e., subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of pr