Treatments and/or Procedures

Study Criteria

Inclusion Criteria:

  -  Subjects must be refractory to, or intolerant of, established therapy known to provide
     clinical benefit for their conditions, or where subjects refuse existing therapies.

  -  Subjects must have measurable disease (RECIST v 1.1) or patients may have bone
     metastatic disease evaluable by Prostate Cancer Working Group 2 (PCWG2) for subjects
     with metastatic castration-resistant prostate cancer (CRPC) or according to tumor
     evaluation criteria best suitable and accepted for the tumor type evaluated.

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

  -  Platelets >= 100 x 10^9/L (For patients with hepatocellular carcinoma, platelets >= 70
     x 10^9/L).

  -  Hemoglobin >= 9 g/dL.

  -  Absolute neutrophil count (ANC) >= 1.5 x 10^9/L.

  -  White blood cell (WBC) >= 3 x 10^9/L.

  -  Alanine transaminase (ALT) =< 2.5 x upper normal limit (ULN) (=< 5 x ULN for subjects
     with documented metastatic disease to the liver).

  -  Aspartate aminotransferase (AST) =< 2.5 x ULN (=< 5 x ULN for subjects with documented
     metastatic disease to the liver).

  -  Alkaline phosphatase < 4 x ULN.

  -  Total bilirubin =< 1.5 x ULN (In the expansion cohort, subjects with Gilbert's
     syndrome [hereditary indirect hyperbilirubinemia] who must have a total bilirubin of
     =< 3 x ULN).

  -  Albumin >= 3 g/dL.

  -  Serum creatinine =< 2 x upper limit of normal (ULN) or estimated creatinine clearance
     >= 30 ml/min as calculated using the Cockcroft-Gault formula.

  -  Subject has recovered to grade =< 1 by the National Cancer Institute Common
     Terminology Criteria for Adverse Events, version 4.03 (NCI-CTCAE v 4.03) from the
     effects of recent surgery, radiotherapy, chemotherapy, hormonal therapy, or other
     targeted therapies, with the exception of alopecia. The exceptions for such effects
     are allowed lab values of =< grade 2 specified elsewhere in these inclusion criteria.

  -  Life expectancy of at least 12 weeks.

  -  Negative serum pregnancy test in women of childbearing potential within 7 days of
     first dose of treatment and patients of child-bearing potential must agree to use
     effective contraception during and after 90 days post dose. A woman of childbearing
     potential is defined as a premenopausal female capable of becoming pregnant. This
     includes women on oral, injectable or mechanical contraception; women who are single
     and women whose male sexual partners have been vasectomized or whose male sexual
     partners have received or are utilizing mechanical contraceptive devices.

  -  Subjects must have biopsiable disease. For Arms A, B, and C, subjects must have at
     least two lesions amenable to biopsy and response evaluation. For Arm D subjects
     should have at least three lesions amenable to biopsy, response evaluation, and
     radiation. Tumor lesions used for biopsy should not be lesions used as RECIST target
     lesions. However, if patients in Arm D do not have three separate lesions, patients
     will be eligible if there are two lesions, in which one is > 2 centimeters (short
     axis) and can be used for both biopsy and response evaluation.

  -  Subjects must give informed consent according to the rules and regulations of the
     individual participating sites.

Exclusion Criteria:

  -  Subjects with primary central nervous system (CNS) tumor or CNS tumor involvement.
     However, subjects with metastatic CNS tumors may participate in this study if the
     subject is:

       -  > 4 weeks from prior therapy completion (including radiation and/or surgery)

       -  Clinically stable with respect to the CNS tumor at the time of study entry

       -  Not receiving steroid therapy in treating CNS tumor or CNS tumor involvement

       -  Not receiving anti-convulsive medications (that were started for brain
          metastases).

  -  Major surgery, radiation therapy or systemic anti-cancer therapy within 4 weeks of
     study drug administration (6 weeks for mitomycin C or nitrosoureas). Palliative
     radiotherapy to a limited field is allowed after consultation with the medical monitor
     at any time during study participation, including during screening, unless it's
     clearly indicative of disease progression.

  -  Subjects with prior anti-PD-1, anti-PD-L1 treatment. For Arms A and D, subjects may
     not have had prior 4-1BB treatment. For Arm B, subjects may not have had prior OX40
     treatment. For Arm C, subjects may not have had prior 4-1BB or OX40 treatment.

  -  Diagnosis or recurrence of invasive cancer other than the present cancer within 3
     years (except basal or squamous cell carcinoma of the skin that has been definitively
     treated).

  -  Clinically significant (i.e., active) cardiovascular disease: cerebral vascular
     accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months
     prior to enrollment), unstable angina, congestive heart failure (>= New York Heart
     Association classification class II), or serious cardiac arrhythmia requiring
     medication.

  -  Active infection requiring systemic therapy.

  -  Treatment with an investigational anti-cancer study drug within 4 weeks prior to study
     drug administration date.

  -  Concurrent therapy with approved or investigational anticancer therapeutics.

  -  Known prior severe hypersensitivity to investigational product(s) or any component in
     its formulations, including known severe hypersensitivity reactions to monoclonal
     antibodies (NCI CTCAE v 4.03 grade >= 3).

  -  Current use of immunosuppressive medication, EXCEPT for the following: a. intranasal,
     inhaled, topical steroids, or local steroid injection (e.g., intra-articular
     injection); b. systemic corticosteroids at physiologic doses =< 10 mg/day of
     prednisone or equivalent; c. steroids as premedication for hypersensitivity reactions
     (e.g., computed tomography [CT] scan premedication).

  -  Active autoimmune disease that might deteriorate when receiving an immuno-stimulatory
     agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid
     diseases not requiring immunosuppressive treatment are eligible.

  -  Prior organ transplantation including allogenic stem-cell transplantation.

  -  Known history of testing positive for human immunodeficiency virus (HIV) or known
     acquired immunodeficiency syndrome.

  -  Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive
     HBV surface antigen or HCV ribonucleic acid (RNA) if anti-HCV antibody screening test
     positive).

  -  Vaccination (live attenuated virus) within 4 weeks of the first dose of avelumab and
     while on trials is prohibited except for administration of inactivated vaccines.

  -  Persisting toxicity related to prior therapy (NCI CTCAE v. 4.03 Grade > 1); however,
     alopecia, sensory neuropathy grade =< 2, or other grade =< 2 not constituting a safety
     risk based on investigator's judgment are acceptable.

  -  Other severe acute or chronic medical conditions including colitis, inflammatory bowel
     disease, pneumonitis, pulmonary fibrosis or psychiatric conditions including recent
     (within the past year) or active suicidal ideation or behavior; or laboratory
     abnormalities that may increase the risk associated with study participation or study
     treatment administration or may interfere with the interpretation of study results
     and, in the judgment of the investigator, would make the patient inappropriate for
     entry into this study.

  -  Medical, psychological or social conditions that may interfere with the patient's
     participation in the study or evaluation of the study results.

  -  Pregnancy or lactation.

  -  Men whose partner is a woman of child-bearing potential, (i.e. biologically able to
     conceive), and who is not employing two forms of highly effective contraception.
     Highly effective contraception (e.g. male condom with spermicide, diaphragm with
     spermicide, intra-uterine device) must be used by both sexes during the study and must
     be continued for 90 days after the end of study treatment. Women of child-bearing
     potential is defined as sexually mature women who are not surgically sterile or who
     have not been naturally postmenopausal for at least 12 consecutive months (e.g., who
     has had menses any time in the preceding 12 consecutive months).

  -  A diagnosis of active scleroderma, lupus, or other rheumatologic disease which in the
     opinion of the treating radiation oncologist precludes safe radiation therapy.

  -  Has had prior radiation therapy within the past 3 months where the high dose area of
     the prior radiation would overlap with the high dose area of the intended radiation
     based on the judgement of the treatment oncologist.