Inclusion Criteria:

- Patients who have MM undergoing autologous or syngeneic hematopoietic transplantation

- Patients must meet Salmon and Durie criteria for initial diagnosis of MM

- Transplant will be offered to patients with stage II or III MM

- Measurable disease, defined as serum monoclonal protein >= 0.2 g/dl or Bence Jones
protein >= 200 mg/24 h

- Karnofsky >= 70 or Eastern Cooperative Oncology Group (ECOG) 0-2

- Life expectancy is not severely limited by concomitant illness

- Left ventricular ejection fraction >= 50%

- No uncontrolled arrhythmias or symptomatic cardiac disease

- Forced expiratory volume in one second (FEV1), forced vital capacity (FVC), and
diffusion capacity of carbon monoxide (DLCO) >= 50%

- No symptomatic pulmonary disease

- Human immunodeficiency virus (HIV) negative

- Bilirubin < 2 mg/dl

- Serum glutamic pyruvate transaminase (SGPT) < 2.5 x normal

- Creatinine clearance >= 60 cc/min, estimated or measured

- Signed informed consent

Exclusion Criteria:

- Pregnant or lactating females

- Uncontrolled infection

- Planned tandem autologous/reduced intensity allograft

- Insufficient PBSC for an autologous transplant (< 3.0 x 10^6 CD34+ cells/kg total)

- Prior autologous transplant

- Non-secretory myeloma and patients who are in a complete response or near complete
response after conventional therapy

- Patients unwilling to practice adequate forms of contraception if clinically
indicated

- Male patients on study need to be consulted to use latex condoms, even if they have
had a vasectomy, every time they have sex with a woman who is able to have children

- Patients with history of seizures

- Patients receiving antihypertensive therapy that cannot be stopped for 24 hours
preceding amifostine treatment