Inclusion Criteria:

Each patient must meet all of the following inclusion criteria to be enrolled in the
study:

- Has a histologically or cytologically confirmed metastatic and/or advanced malignancy
(including lymphomas but excluding malignancies with extensive bone marrow
involvement such as leukemias and multiple myeloma) for which standard treatment does
not offer curative or life-prolonging potential

- Aged 18 years or more

- Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

- Expected survival longer than 3 months from enrollment in the study

- Radiographically or clinically evaluable tumor; however, measurable disease is not
required for participation in this study

- Suitable venous access for the conduct of blood sampling for determination of MLN8054
plasma concentrations

- Willingness to have serial skin punch biopsies obtained and, if feasible, to have
serial biopsies of tumor tissue obtained before and following the first dose of
MLN8054 Note: Once the relationship between drug exposure and inhibition of Aurora A
kinase activity has been established, patients subsequently enrolled in the study
will not be required to undergo either tumor or skin biopsies.

8. Recovered from the reversible effects of prior antineoplastic therapy with at
least 4 weeks elapsed since the last exposure to cytotoxic chemotherapy or
radiotherapy and at least 6 weeks elapsed since exposure to nitrosoureas or mitomycin
C. Patients treated with fully human monoclonal antibodies must not have received
treatment with such antibodies for at least 6 weeks, and those treated with chimeric
monoclonal antibodies must not have received treatment with such antibodies for at
least 4 weeks. Patients treated with noncytotoxic small molecule drugs (eg, tyrosine
kinase inhibitors such as Tarceva and hormonal agents such as Femara®) must not have
received treatment with these drugs for at least 2 weeks before the first dose of
MLN8054 is given.

- Male patients must use an appropriate method of barrier contraception (ie, condoms)
and inform any sexual partner that she must also use a reliable method of
contraception (eg, a hormonal contraceptive, an intrauterine device, or diaphragm
with spermicide) during the study and for 3 months after the last dose of study
treatment.

- Female patients must be postmenopausal, surgically sterilized, or willing to use
reliable methods of birth control (eg, a hormonal contraceptive, an intrauterine
device, diaphragm with spermicide, or abstinence) during the study and for 3 months
after the last dose of study treatment. They should inform any male sexual partner
to use an appropriate method of barrier contraception (ie, condoms) as well.

- Able to give informed consent before the conduct of any study-related procedure not
part of normal medical care and able to comply with the protocol

Exclusion Criteria:

Patients meeting any of the following exclusion criteria are not to be enrolled in the
study:

- Pregnant or lactating

- Major surgery within the 21 days preceding the first dose of study treatment

- Infection requiring antibiotic therapy within the 7 days preceding the first dose of
study treatment

- Life-threatening illness unrelated to cancer

- Ongoing nausea or vomiting greater than Grade 1 in severity. Patients who require
ongoing treatment with metoclopramide to control nausea or vomiting, to the point
that it is Grade 1 or less in severity, are allowed to participate in this trial.

- Diarrhea greater than Grade 1 in severity. Patients who require ongoing therapy with
an antimotility agent to control diarrhea to a Grade 1 or lower level are not allowed
to participate in this trial.

- Known GI disease that could interfere with the oral absorption or tolerance of
MLN8054

- Difficulty swallowing capsules

- Inability to remain nothing by mouth (NPO), except for water and prescribed
medications, for 2 hours preceding and 2 hours following each dose of MLN8054

- Received more than 4 previous cytotoxic chemotherapeutic regimens including regimens
used as adjuvant or neo-adjuvant therapies. There is no limit on the number of
noncytotoxic therapies (eg, hormonal and immunologic) that patients may have
received. Tyrosine kinase inhibitors (eg, Tarceva and Iressa®) are considered
noncytotoxic compounds.

- Prior treatment with high-dose chemotherapy, defined as chemotherapy requiring the
use of peripheral blood or bone marrow stem cell support for hematopoietic
reconstitution

- Prior treatment with radiation therapy involving greater than or equal to 25% of the
hematopoietically active bone marrow

- Clinical and/or radiographic evidence of cerebral metastases. However, patients who
have a history of CNS metastasis but have no radiographic or clinical evidence of
residual tumor (eg, following complete surgical resection) are not excluded from
participation in this study.

- Absolute neutrophil count <1.5 x 106/ul; platelet count <100 x 106/ul.

- Serum creatinine >1.6 mg/dL or a measured or estimated (Cockcroft-Gault formula)
creatinine clearance <30 mL/minute

- Bilirubin >1.25 times the upper limit of the normal range (ULN); aspartate
aminotransferase (AST)/alanine aminotransferase (ALT) >2 times the ULN, and alkaline
phosphatase (ALP) >2 times the ULN. Both the AST and ALP may be elevated up to 5
times the ULN if their elevation can be reasonably ascribed to the presence of
metastatic disease to liver and/or to bone; however, the ALT must in all
circumstances be <2 times the ULN.

- Abnormalities or arrhythmias on 12-lead electrocardiogram (ECG) that, in the opinion
of the investigator, are considered to be clinically significant

- Known or suspected human immunodeficiency virus (HIV) positive or hepatitis B surface
antigen-positive status or known or suspected active hepatitis C infection

- Known or suspected disorder of bilirubin metabolism or excretion including, but not
limited to, Gilbert's syndrome, Crigler-Najjar syndrome, Dubin-Johnson syndrome, and
Rotor syndrome

- Inclusion in a trial of an investigational drug in the previous 4 weeks

- Admission of alcohol abuse or an inability to restrict consumption of alcohol to no
more than 1 standard unit of alcohol per day during the study and for 21 days from
the last dose of study treatment. A standard unit of alcohol is defined as one 12 oz
beer, 1.5 oz of 80 proof alcohol, or one 6 oz glass of wine.

Note: criteria 22, 23, and 24 apply only to patients in whom biopsy of tumor tissue is
planned.

- aPTT and/or PT exceeding the ULN

- Known bleeding diathesis or history of abnormal bleeding

- Ongoing therapy with an anticoagulant (eg, aspirin, plavix, coumadin, heparin)