Patients must have a diagnosis of biopsy-proven diagnosis of AL amyloidosis according to the following standard criteria:\r\n* Histochemical diagnosis of AL amyloidosis, as based on tissue specimens with Congo red staining with exhibition of an apple-green birefringence and immunohistochemistry\r\n* If clinical and laboratory parameters insufficient to establish AL amyloidosis or in cases of doubt, amyloid typing may be necessary\r\n* Measurable disease as defined by serum differential free light chain concentration (dFLC, difference between amyloid forming [involved] and non amyloid forming [uninvolved] free light chain [FLC]) ? 50 mg/L)\r\n* Systemic amyloid organ involvement including renal, cardiac, gastrointestinal (GI) and/or nervous system involvement as well as soft tissue disease Known amyloid involvement COHORT B: biopsy proven light chain amyloidosis with organ involvement requiring therapy Non-secretory MM or known amyloid light-chain (AL) amyloidosis Biopsy-proven histochemical diagnosis of amyloid light-chain (AL) amyloidosis based on tissue specimens with Congo red staining or other histologic stain; thioflavin T or S, or crystal violet; tandem mass spec or immunohistochemistry (IHC) confirmation of immunoglobulin-derived amyloidosis is encouraged; cases in which histochemical confirmation is lacking need to be discussed with one of the Multiple Myeloma Research Foundation (MMRF) protocol chair/co-chairs Measurable hematologic disease as defined by:\r\n* Serum differential free light chain concentration (dFLC, difference between amyloid forming [involved] and non-amyloid forming [uninvolved] free light chain [FLC]) >= 50 mg/L) Measurable disease of amyloid light-chain (AL) amyloidosis as defined by at least one of the following: Non-secretory MM or known amyloid light-chain (AL) amyloidosis Light chain (AL) amyloidosis patients with Mayo cardiac stage III (defined as N-terminal proB-type natriuretic peptide measurement [proBNP] > 332 ng/L and cardiac troponin [cTnT] > 0.035 ug/L) Systemic amyloid light chain amyloidosis If clinical and laboratory parameters insufficient to establish AL amyloidosis or in cases of doubt, amyloid typing may be necessary. Objective, measurable major (cardiac or renal) organ amyloid involvement as defined as follows (amyloid involvement of at least 1 required): Primary systemic AL (immunoglobulin light chain) amyloidosis Patients who have not been treated or who have received chemotherapy within 6 months, or SCT within 12 months, for the light-chain producing hematologic disease causing AL amyloidosis, at the time of the first dose of NEOD001 (month 1 day 1) Known amyloid involvement Patients must have a confirmed diagnosis of amyloid light-chain (AL) amyloidosis based on accepted clinical and laboratory criteria Demonstrated clonal population of plasma cells in the bone marrow or positive immunohistochemical stain with anti-light chain anti-sera of amyloid fibrils Primary systemic amyloid light (AL) chain amyloidosis (a build-up of amyloid light chain proteins in the blood) Histopathology of amyloidosis or light chain deposition disease based on detection by polarizing microscopy of green bi-refringent material in Congo red-stained tissue specimens or characteristic electron microscopy appearance or immunohistochemical stain with anti-light chain anti-sera Presence of primary (light chain) amyloidosis. Histologically-proven AL amyloidosis, confirmed by positive Congo red stain with green birefringence on polarized light microscopy with evidence of measurable clonal disease that requires active treatment as defined below: Documented active systemic amyloid light chain amyloidosis. Primary systemic amyloid light-chain (AL) (immunoglobulin light chain) amyloidosis Documented systemic light chain amyloidosis.