Inclusion Criteria:

1. B cell lymphoma patients must have had their diagnosis confirmed histologically. Plasma cell leukemia (PCL) patients must have peripheral clonal plasma cells >20% of peripheral WBC and >2 x 109/L. Multiple myeloma and PCL patients must have been diagnosed by having met all three of the following IMWG criteria:
   • Clonal bone marrow plasma cells >10%
   • Presence of serum and/or urinary M-protein or, if absent, kappa or lambda serum FLC must be > 10 mg/dl accompanied by an abnormal kappa to lambda ratio (<0.26 or >1.65)
   • Evidence of end-organ damage that can be attributed to the underlying plasma cell proliferative disorder, specifically, one or more of the following:
     • Hypercalcemia: serum calcium >11.5 mg/100 mL
     • Renal insufficiency: serum creatinine >2mg/dL
     • Anemia: normochromic, normocytic with a hemoglobin value >2 g/100 mL below the lower limit of normal or a hemoglobin value <10 g/100 mL
     • Bone lesions: lytic lesions, severe osteopenia, or pathologic fractures
2. B cell lymphoma patients must have measurable disease defined as at least one lesion that can be accurately measured for response in at least two perpendicular dimensions. Multiple myeloma patients must have measurable disease defined by the following:
   • Serum M-protein ≥0.5g/dL or urine M-protein ≥ 200 mg/24 hours by protein electrophoresis
   • If neither serum nor urine M-protein meet the criteria above, then kappa or lambda serum FLC must be ≥10 mg/dL accompanied by an abnormal kappa to lambda ratio (<0.26 or >1.65) (Serum FLC should only be used for patients without measurable serum or urine M-protein spike.)
   • If neither of the above criteria are met, the presence of plasmacytomata measurable radiographically (CT, PET or MRI) or by direct measurement.
3. Have relapsed or refractory disease after two or more prior treatment lines, each of which may have consisted of either single or multiple regimens. The investigators will ensure that patients have had the benefit of standard treatments before considering the SNS01-T clinical trial.
4. Be at least 2 weeks beyond the last therapy and have recovered from acute toxicities of prior therapies
5. Have Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2
6. Have life expectancy of at least 3 months
7. Be ≥18 years of age and willing to provide written informed consent
8. For women and men of childbearing potential, have used effective contraceptive methods for at least 4 weeks prior to dosing and agree to continue using such methods during the study, and for at least 4 weeks after completing the study
9. For women of childbearing potential, have a negative serum pregnancy test within 24 hours before the initiation of SNS01-T therapy
10. Have an absolute neutrophil count >1,000/mm3
11. Have a platelet count >75,000/mm3
12. Have total bilirubin <2.0 mg/dL
13. Have aspartate aminotransferase and alanine aminotransferase <3 times the upper limit of normal
14. Have serum creatinine ≤3 times the upper limit of normal
15. Have hemoglobin ≥8.0 g/dL

Exclusion Criteria:

1. Have presence of nonsecretory myeloma
2. Have an indolent lymphoma such as follicular lymphoma unless the disease is rapidly progressing
3. Requires renal dialysis
4. Have New York Heart Association Class III-IV heart failure classification
5. Have CNS or leptomeningeal disease
6. Have an active infection or serious comorbid medical condition
7. Be receiving other concurrent anticancer agents or therapies
8. Be receiving other concurrent investigational therapies or have received investigational therapies within 4 weeks of screening or 5 half-lives, if known, whichever is shorter
9. Be eligible to receive any other standard therapy available that is known to extend life expectancy
10. Be currently receiving steroids unless equivalent to 20 mg of prednisone or less
11. Be receiving or have received heparin therapeutically within two days before and after treatment with SNS01-T
12. Be pregnant or nursing