The purpose of this study is to assess the safety and tolerability of escalating doses of SNS-032, given in 3 weekly administrations per cycle and to identify a recommended Phase 2 dose.

Other objectives of this study include measuring pharmacokinetics (how long the drug can be measured in the body) and identifying potential biomarkers.

Inclusion Criteria:

• Cytologically or histologically confirmed chronic lymphocytic leukemia (CLL), mantle cell lymphoma (MCL), or multiple myeloma (MM).
• Evidence of relapsed disease
• Measurable disease
• Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0 or 1

Exclusion Criteria:

• Prior treatment with SNS-032 injection (previously known as BMS-387032)
• Pregnant or breastfeeding
• Unwilling to use an approved, effective means of contraception according to the study site's standards
• Use of therapeutic anticoagulation agents
• Prior allogeneic bone marrow transplantation
• Prior chemotherapy, monoclonal antibodies, investigational agents, or radiation therapy within 21 days before the first dose; nitrosoureas and mitomycin are not permitted for at least 42 days before the first dose.
• Prior pelvic radiation therapy or radiation to > 25% of bone marrow reserve
• Any other medical, psychological, or social condition that would contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures

Please note: There are additional inclusion/exclusion criteria for this study. Please contact the study center for additional information and to determine if the patient meets all study criteria.