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 Follicular lymphoma

- B-cell Marginal zone lymphoma

- Diffuse large B-cell lymphoma

- B-cell Mantle cell lymphoma

- B-cell Small lymphocytic lymphoma (SLL)

- B-Cell Chronic lymphocytic leukemia (B-CLL)

- Multiple myeloma

- Waldenstrom's macroglobulinemia

- Noncutaneous peripheral T-cell lymphoma not otherwise specified (PTCL-NOS)

- Angioimmunoblastic T-cell lymphoma (AITL), anaplastic large cell lymphoma,
enteropathy associated T-cell lymphoma (EATCL), NK lymphoma (NKL)

- 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:

- Pregnant or lactating

- Treatment with clinically significant enzyme inducers within 14 days prior to the
first dose of MLN8237 as specified in the protocol

- 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.

- Patients who fail to meet laboratory values as specified in the protocol during the
screening period