The main purpose of this study is to learn more about how the study drug called galunisertib affects the immune system in participants with cancer. The study treatment is expected to last about six months for each participant, not including screening or follow-up.

Inclusion Criteria:

• Have a confirmed diagnosis of advanced, refractory solid tumors and tumor progression or treatment intolerance to at least 1 prior therapy.

• Have measurable disease that is amenable to a radiographic or ultrasound-guided biopsy or may be biopsied in the office without radiologic guidance.

• Have a performance status of ≤2 on the Eastern Cooperative Oncology Group (ECOG) scale.

• Have discontinued all disease-modifying therapy for the primary cancer for 28 days prior to initiation of study treatment.

• Hepatic: bilirubin ≤1.5 times upper limits of normal (ULN), alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤3.0 times ULN. For participants with tumor involvement of the liver, AST and ALT equaling

  ≤5.0 times ULN are acceptable. Alkaline phosphatase ≤5.0 times ULN for participants with tumor involvement of the bone is acceptable.

• Have adequate renal function, defined as serum creatinine levels ≤2.0 ULN or calculated creatinine clearance >45 mL/min.

• Male and female participants with reproductive potential must use an approved contraceptive method, if appropriate (for example, intrauterine device, birth control pills, or barrier device) during and for 6 months after discontinuation of study treatment.

• Women of childbearing potential must have a negative beta-human chorionic gonadotropin pregnancy test documented within 7 days prior to treatment. Have given written informed consent prior to any study-specific procedures.

• Are willing and able to comply with study procedures and instructions, including completion of diaries.

• Must have received at least 1 prior approved immunotherapy or chemotherapy; however, not within 28 days of the initial dose of study drug. May have received prior radiotherapy for their malignancy.

• May have received treatment with an investigational product.

Exclusion Criteria:

• Are enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study within 28 days of the initial dose of study drug.

• Have moderate or severe cardiac disease:

  • Have the presence of cardiac disease, including a myocardial infarction within 6 months prior to study entry, unstable angina pectoris, New York Heart Association Class III/IV congestive heart failure, or uncontrolled hypertension.
  • Have documented major electrocardiogram (ECG) abnormalities (not responding to medical treatments) at the investigator's discretion (for example, symptomatic or sustained atrial or ventricular arrhythmias, second- or third-degree atrioventricular block, complete bundle branch block, ventricular hypertrophy, or recent myocardial infarction).
  • Have major abnormalities documented by echocardiography (ECHO) with Doppler (for example, moderate or severe heart valve function defect and/or left ventricular ejection fraction <50%, evaluation based on the institutional lower limit of normal).
  • Have predisposing conditions that are consistent with development of aneurysms of the ascending aorta or aortic stress (for example, family history of aneurysms, Marfan-Syndrome, bicuspid aortic valve, evidence of damage to the large vessels of the heart documented by computed tomography (CT) scan with contrast).

• Are women who are pregnant or lactating.

• Have a serious concomitant systemic disorder (for example, active infection including human immunodeficiency virus [HIV], hepatitis C virus [HCV], hepatitis B virus [HBV] [ie, positive hepatitis B surface antigen [+HBsAg]]), or an autoimmune disease.

• Have a second primary malignancy or any history in any time frame of a prior malignancy.

• Are unwilling or unable to participate in, or do not have tissue adequate for participation in the biomarker analyses in the study.