For cancer cells to grow, they need to have nutrients supplied to them through blood vessels. The study drug, ACE-041, is designed to work by blocking the growth of those blood vessels and preventing cancer cells from growing. The purpose of this study is to establish safe dose levels of ACE-041 in patients with advanced solid tumors or relapsed/refractory multiple myeloma following multiple dose administration. This study will also evaluate if ACE-041 has an effect on tumors.

Inclusion Criteria:

• Diagnosis of metastatic or unresectable advanced solid tumors (solid tumors must be measurable) or relapsed/refractory multiple myeloma for which the disease has progressed despite available standard therapies or for which no standard therapy exists.
• Life expectancy of at least 12 weeks.
• Eastern Cooperative Oncology Group (ECOG) Performance status of 0, 1, or 2 (not declining within 2 weeks prior to study day 1).

Exclusion Criteria:

• Central nervous system (CNS) metastases.
• Chemotherapy or other anti-cancer therapy within 4 weeks prior to study day 1, and/or nitrosoureas within the 6 weeks prior to study day 1.
• Lack of recovery from all toxic effects of previous chemotherapy, radiation therapy, biologic therapy, and/or experimental therapy with the exception of alopecia.
• Radiation therapy within 4 weeks prior to study day 1.
• Clinically significant pulmonary, cardiovascular, endocrine, neurologic, gastrointestinal or genitourinary disease unrelated to underlying solid tumor or multiple myeloma
• Significant cardiac risk (e.g. history of myocardial infarction, unstable angina, pulmonary hypertension, clinically significant arrhythmia, congestive heart failure within 1 year prior to study day 1).
• Diagnosis or family history of hereditary hemorrhagic telangiectasia.
• Major surgery within 6 weeks prior to study day 1.
• Parenteral antibiotics, or any life-threatening or active infection requiring parenteral antibiotic therapy within 1 month prior to study day 1.
• Therapeutic anti-coagulation.
• Uncontrolled hypertension.
• Autoimmune or hereditary hemolysis.
• Clinically significant gastrointestinal bleeding or any other clinically significant active bleeding within 3 months prior to study day 1.
• Treatment with another investigational drug or device, or approved therapy for investigational use within 28 days prior to study day 1.
• Pregnancy or lactation for female patients.