Inclusion Criteria:

• Relapsed or refractory disease and a histologically or cytologically confirmed hematological malignancy of the following type for which standard curative treatment does not exist or is no longer effective:

  • B-Cell Non-Hodgkins Lymphoma: diffuse large cell lymphoma, follicular lymphoma, marginal zone lymphoma, mantle cell lymphoma
  • B-Cell Chronic lymphocytic leukemia (CLL)/ small lymphocytic leukemia (SLL)
  • Multiple myeloma
  • Waldenstrom's macroglobulinemia
• Subjects with diffuse large B-cell lymphoma must have failed, be ineligible for, or have refused an autologous stem cell transplant. There is no restriction regarding the maximum number of prior regimens.
• Aged 18 years or older
• Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2
• Radiographically or clinically evaluable disease for Part 1 of this study and measurable disease for Part 2 of this study
• Suitable venous access for the conduct of blood sampling for MLN8237 PK
• Recovered from the reversible effects of prior antineoplastic treatment (with the exception of alopecia and Grade 1 neuropathy)

Exclusion Criteria:

• Prior allogeneic bone marrow (or other organ) transplantation
• Newly diagnosed or uncontrolled cancer-related CNS disease
• Systemic antineoplastic treatment within 21 days preceding the first dose of study treatment. Exceptions requiring a 42-day recovery period from last treatment include: Nitrosoureas, mitomycin C or Rituximab, alemtuzumab (Campath®), or other unconjugated therapeutic antibody (21 days if clear evidence of progressive disease)
• Treatment with radioimmunoconjugates or toxin immunoconjugates such as ibritumomab tiuxetan (Zevalin™), or tositumomab (Bexxar®) within 56 days preceding the first dose of study treatment
• Antineoplastic treatment with glucocorticoids within 21 days preceding the first dose of study treatment
• Radiotherapy involving <25% of the hematopoietically active bone marrow within 21 days preceding first dose of study treatment
• Radiotherapy involving ≥25% of the hematopoietically active bone marrow within 42 days preceding first dose of study treatment
• Inability to swallow capsules or known GI disease or GI procedures that could interfere with the oral absorption or tolerance of MLN8237. Examples include, but are not limited to, partial gastrectomy, history of small intestine surgery, and celiac disease.
• History of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness such as severe chronic obstructive pulmonary disease
• Known or suspected human immunodeficiency virus (HIV) positive or hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection. Testing is not required in the absence of clinical findings or suspicion.