The goal of this clinical trial is to determine the toxicity and also the efficacy of a treatment that includes the following treatment: Two medications, bortezomib and dexamethasone (or BD), followed by autologous stem cell transplantation, and a prolonged course of treatment with bortezomib and dexamethasone after transplantation. This type of treatment has been very effective in multiple myeloma. However, there is little experience with this treatment in patients who have Monoclonal Immunoglobulin Deposition Disease (MIDD) or amyloidosis. The investigators and others have treated patients who have MIDD and amyloidosis with bortezomib and autologous stem cell transplantation and have had success with this treatment. But the combination of autologous transplant with BD given before and after the transplant is a new way of treating these diseases, which the investigators believe will be very effective.

Inclusion Criteria:

• Age > or = to 18
• New diagnosis of MIDD or AL amyloidosis based on pathologic findings confirmed at Memorial Sloan Kettering Cancer Center.
• Patients must show the ability to understand the investigational nature of the treatment and to give voluntary informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care.
• Female subject is either postmenopausal for at least 1 year before the screening visit, is surgically sterilized or if they are of childbearing potential, agree to practice 2 effective methods of contraception from the time of signing the informed consent form through 30 days after the last dose of bortezomib, or agree to completely abstain from heterosexual intercourse.
• Male subjects, even if surgically sterilized (i.e., status post-vasectomy) must agree to 1 of the following: practice effective barrier contraception during the entire study treatment period and through a minimum of 30 days after the last dose of study drug, or completely abstain from heterosexual intercourse.
• Adequate organ function defined as follows: Absolute granulocytes > 1,000/mm3 and platelets > 70,000/mm3, unless low granulocyte and platelets counts are due to multiple myeloma; total bilirubin < 1.5 ULN; AST, ALT, and alkaline phosphatase < 3 times upper limit of laboratory normal; LVEF > 50% by MUGA or ECHO (the method used at baseline must be used for later monitoring); DLCO > 50 % confirmed at MSKCC; elevated creatinine is not a contraindication to enrollment
• Performance status (ECOG) < or = to 2

Exclusion Criteria:

• Patient has received other investigational drugs with 14 days before enrollment
• Prior initial treatment chemotherapy for MIDD, AL amyloidosis or multiple myeloma with the exception of one cycle of high dose dexamethasone
• Prior bortezomib treatment
• Myocardial infarction within 6 months prior to enrollment or New York Heart Association Class III or IV heart failure (see Appendix 20.2), uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening has to be documented by the investigator as not medically relevant.
• Pregnant or lactating women are ineligible. A pregnancy test will be performed on each fertile premenopausal female 2 weeks prior to entry into the study. Treatment may not begin until the results of the pregnancy test are ascertained. All patients (men and women) must agree to use medically approved contraceptive measures for at least 4 weeks before starting therapy, during therapy, and for at least 3 months after therapy has stopped.
• Pre existing neuropathy, sensory or neuropathic pain findings, grade 2 or higher on the NCI CTC neurotoxicity scale.
• Concurrent active malignancy other than non melanoma skin cancers or carcinoma in situ of the cervix. Patients with previous malignancies, but which have not required anti tumor treatment within the preceding 24 months will be allowed to enter the trial. Patients with a history of a T1a or b prostate cancer (detected incidentally at TURP and comprising less than 5% of resected tissue) may participate if the PSA has remained within normal limits since TURP.
• Patients with known HIV positivity or AIDS related illness. This is based upon the possibility of increasing HIV viral load with therapy
• Any other medical condition or reason that, in the principal investigator's opinion, makes the patient unsuitable to participate in a clinical trial
• Patients with a history of hypersensitivity reactions attributed to bortezomib, boron, or mannitol.
• Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy.