This is a study to determine the clinical benefit (how well the drug works), safety, and tolerability of combining varlilumab and nivolumab (also known as Opdivo® , BMS-936558). Both drugs target the immune system and may act to promote anti-cancer effects.

Varlilumab is a fully human monoclonal antibody that binds to a molecule called CD27 found on certain immune cells and may act to promote anti-tumor effects.

Nivolumab is a fully human monoclonal antibody that binds to a molecule called PD-1 on immune cells and promotes anti-tumor effects.

Eligible patients that enroll in the dose escalation portion of the study will be assigned to one of three dose levels of varlilumab in combination with 3 mg/kg of nivolumab. The first phase of the study will test the safety profile of the combination and determine which dose will be studied in Phase ll of the overall study.

During Phase ll, depending on cancer type, groups of patients will be enrolled and receive varlilumab at a dose of either 3 mg/kg every 2 weeks, 3 mg/kg every 12 weeks, or 0.3 mg/kg every 4 weeks in combination with nivolumab at 240 mg.

All patients enrolled in the study will be closely monitored to determine if there is response to the treatment as well as for any side effects that may occur.

Key Inclusion Criteria:

1. Histologically-diagnosed advanced (unresectable and/or metastatic) Non-small Cell Lung Cancer (Phase l only), Melanoma (Phase l only), Colorectal, Head and Neck SCC (squamous cell carcinoma), Ovarian Cancer, Glioblastoma or Renal Cell Carcinoma.

   • 1a. Head and Neck

   Stage III/IV squamous cell carcinoma; Tumor progression or recurrence within 6 months of last dose of platinum therapy in the adjuvant, primary, recurrent or metastatic setting (or within 9 months if the patient received > 1 platinum-based chemotherapy regimen in the metastatic setting). Active brain metastases or leptomeningeal metastases are excluded; nasopharyngeal cancer, confirmed recurrent or metastatic carcinoma of the nasopharynx and salivary gland or non-squamous histologies are also excluded.

   • 1b. Ovarian

   Recurrent or persistent epithelial ovarian, fallopian tube or primary peritoneal carcinoma requiring original or subsequent relapse histologic documentation. A platinum-taxane based chemotherapy regimen as frontline therapy must have been completed.

   Any histologic diagnosis of borderline, low malignant potential epithelial carcinoma are excluded.

   • 1c. Colorectal Cancer -Enrollment Completed

   Metastatic or recurrent; prior treatment progression during, after, or intolerant following the last administration of approved standard therapies (required therapies apply).

   • 1d. Glioblastoma -Enrollment Completed

   Have histologically confirmed World Health Organization Grade IV malignant glioma (glioblastoma).

   • Previous first line therapy with at least radiotherapy and temozolomide.
   • Participants must have shown unequivocal evidence of tumor progression.
   • More than one relapse, secondary glioblastoma and prior treatment with bevacizumab are excluded.

   An interval of at least 12 weeks from the completion of radiation therapy to start of study treatment is required.

   • 1e. Renal Cell Carcinoma

   Have histologically confirmed diagnosis of predominant clear cell renal cell carcinoma.

   • Must have received 1 or 2 prior anti-angiogenic therapies.
   • No more than 5 total previous regimens of systemic therapy, including cytokines and cytotoxic chemotherapy.
   • Disease progression during or after the last treatment regimen and within 6 months before study entry.

2. No more than 5 prior anticancer regimens for advanced (recurrent, locally advanced or metastatic) disease except for patients with GBM which must have first recurrence of GBM by diagnostic biopsy or contrast enhanced magnetic resonance imaging (MRI).

3. Measurable (target) disease.

4. Life expectancy ≥ 12 weeks.

5. If of childbearing potential (male or female), agree to practice an effective form of contraception during study treatment and for at least 23 weeks after for female and 31 weeks after for male following last treatment dose.

Key Exclusion Criteria:

1. History of severe hypersensitivity reactions to other monoclonal antibodies.
2. Prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 antibody.
3. Receipt of anti-CTLA-4 or anti-CD27 antibody within 3 months prior to the planned start of study treatment.
4. Use of any monoclonal based therapies within 2-4 weeks prior to the first dose of study treatment.
5. Chemotherapy within 21 days or at least 5 half-lives (whichever is shorter) prior to the planned start of study treatment.
6. BRAF/MEK inhibitors within 2 weeks prior to the first dose of study treatment.
7. Systemic radiation therapy within 4 weeks, prior focal radiotherapy within 2 weeks, or radiopharmaceuticals (strontium, samarium) within 8 weeks prior to the first dose of study treatment.
8. Use of immunosuppressive medications within 4 weeks or systemic corticosteroids within 2 weeks prior to first dose of study treatment.
9. Other prior malignancy, except for adequately treated basal or squamous cell skin cancer or in situ cancers; or any other cancer from which the patient has been disease-free for at least 3 years.
10. Active, untreated central nervous system metastases.
11. Active autoimmune disease or a documented history of autoimmune disease
12. Active diverticulitis.
13. Interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity.
14. Significant cardiovascular disease