Anti-CD137 and Anti-CTLA-4 Monoclonal Antibody in Patients With Advanced Cancer

Inclusion Criteria: 1. Voluntarily agree to participate by giving signed, dated, and written informed consent prior to any study specific procedures. Participation in pharmacogenomics testing is optional. 2. ≥ 18 years of age. 3. Histologically or cytologically confirmed diagnosis of a solid tumor that is currently metastatic or locally advanced for which no standard therapy is available or standard therapy has failed. 4. Measurable disease on imaging based on RECIST 1.1. 5. Life expectancy of ≥ 3 months and ECOG performance status of 0 or 1. 6. Adequate organ and bone marrow reserve function, as indicated by the following laboratory values: * Adequate hematological function, defined as absolute neutrophil count ≥ 1.5 × 10\^9/L, platelet count ≥ 100 × 10\^9/L, and hemoglobin ≥ 8 g/dL without recent transfusion (defined as a transfusion that has occurred within 2 weeks of the hemoglobin measurement) * Adequate liver function, defined as total bilirubin level ≤ 1.5 × upper limit of normal (ULN), aspartate aminotransferase ≤ 2.5 × ULN, and alanine aminotransferase ≤ 2.5 × ULN, albumin ≥ 3 g/dL, and alkaline phosphatase ≤ 2.5 × ULN or ≤ 5 × ULN for patients with liver metastases * Adequate renal function defined as creatinine ≤ 1.5 × ULN OR measured or calculated creatinine clearance ≥ 40 mL/minute per institutional standard. Assessment methods should be recorded * Adequate coagulation, defined as international normalized ratio or prothrombin time ≤ 1.5 × ULN and activated partial thromboplastin time ≤ 1.5 × ULN (unless patient is receiving anticoagulant therapy) 7. Patients with a history of prior malignancy are eligible if treatment was completed ≥ 2 years prior to the first dose of study treatment and the patient has no evidence of disease. 8. Patients must provide a sufficient and adequate formalin-fixed paraffin-embedded tumor tissue sample (biopsy) collected after the last dose of prior anti-cancer therapy and before the first dose of study treatment from a site not previously irradiated and agree to mandatory on-treatment biopsy if clinically feasible. 9. Female patients of childbearing potential must have a negative serum pregnancy test at screening (within 72 hours of first dose of study medication). Non-childbearing potential is defined as 1 of the following: * ≥ 45 years of age and has not had menses for \> 1 year * Amenorrheic for \> 2 years without a hysterectomy and oophorectomy and follicle-stimulating hormone value in the postmenopausal range upon prestudy (screening) evaluation * Status is post-hysterectomy, -bilateral oophorectomy, or -tubal ligation 10. Female patients of childbearing potential must be willing to use highly effective contraceptive measures starting with the Screening Visit through 90 days after last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception method for the patient. 11. Male patients with a female partner(s) of childbearing potential must agree to use highly effective contraceptive measures throughout the study starting with the Screening Visit through 90 days after the last dose of study treatment is received. Males with pregnant partners must agree to use a condom; no additional method of contraception is required for the pregnant partner. Note: Abstinence is acceptable if this is the established and preferred contraception method for the patient. Specific Melanoma Criteria: Note: these specific criteria below are in addition to the general criteria above and supersede the general criteria in some cases. Inclusion: 1. Histological confirmation of cutaneous melanoma. 2. Progression on or within 24 weeks of stopping treatment with a PD-1/PD-L1 confirmed per Society for Immunotherapy of Cancer (SITC). 3. Patients with BRAF V600-positive tumor(s) should also have received prior treatment with a BRAF inhibitor (alone or in combination with a MEK inhibitor) or have declined targeted therapy. Note: Patients with BRAF V600-positive tumors with no clinically significant tumor-related symptoms nor evidence of rapidly progressive disease are not required to be treated with a BRAF inhibitor (alone or in combination with a MEK inhibitor) based on Investigator's decision. Exclusion Criteria: 1. Currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigation device within 3 weeks of first dose of current study treatment. 2. Received prior systemic cytotoxic chemotherapy, biological therapy, radiotherapy, or major surgery outside of the acceptable washout period prior to first dose of study drug. A 1-week washout is permitted for palliative radiation to non-central nervous system (CNS) disease, with Sponsor approval. The following washout windows are acceptable from prior treatments (i.e., patients with time periods less than the following should be excluded): * Cytotoxic agent ≥ 3 weeks is acceptable (i.e., \< 3 weeks should be excluded) * Monoclonal antibodies ≥ 4 weeks is acceptable (i.e., \< 4 weeks should be excluded) * Proteasome inhibitors or corticosteroids ≥ 2 weeks is acceptable (i.e., \< 2 weeks should be excluded) * Small molecule/tyrosine kinase inhibitor within 14 days or less than 5 circulating half-lives of investigational drug * Having a previous SARS-CoV-2 vaccine \> 7 days before administration. For vaccines requiring more than 1 dose, the full series should be completed prior to Cycle 1 Day 1, when feasible, and when the delay in initiation of study treatment would not put the study patients at risk 3. Patients who have received prior anti-CD137 therapy may be enrolled upon agreement with the Sponsor. 4. Persistent toxicity of NCI-CTCAE version 5.0 Grade \> 1 severity that is related to prior therapy. Note: Sensory neuropathy or alopecia of Grade ≤ 2 are acceptable. 5. Expected to require any other form of systemic or localized antineoplastic therapy while on study (including maintenance therapy with another agent, radiation therapy, and/or surgical resection). 6. History of: * Severe (Grade ≥ 3) hypersensitivity reactions to fully human monoclonal antibodies * Immune-related adverse event requiring treatment with systemic steroids for \> 7 days (refer to Exclusion Criterion #7 for exceptions) excluding Grade 1 or 2 rash * Interstitial lung disease or lung disease which may interfere with the assessment of pneumonitis * Uncontrolled asthma (i.e., ≥ 3 features of partly controlled asthma) * Pneumonitis that has required oral or IV corticosteroids 7. Receiving systemic corticosteroid therapy per Exclusion Criterion #2, or any other form of systemic immunosuppressive medication. Note: Corticosteroid use as a premedication for IV contrast allergies/reactions is allowed. Patients who are receiving daily corticosteroid replacement therapy are also an exception to this rule. Daily prednisone at doses of ≤ 10 mg or equivalent hydrocortisone dose are examples of permitted replacement therapy. Use of inhaled or topical corticosteroids is permitted. 8. CNS tumor, metastasis(es), and/or carcinomatous meningitis identified either on the baseline brain imaging obtained during the Screening Period or identified prior to consent. Note: Patients with history of brain metastases that have been treated may participate provided they show evidence of stable supra-tentorial lesions at screening (defined as 2 brain images, both of which are obtained after treatment to the brain metastases and obtained ≥ 4 weeks apart). In addition, any neurologic symptoms that developed either as a result of the brain metastases or their treatment must have returned to baseline or resolved. Any steroids administered as part of this therapy must be completed ≥ 3 days prior to first dose of study medication. 9. Active or history of autoimmune disease that requires systemic treatment within 2 years of the start of study treatment (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Note: Patients with autoimmune conditions requiring hormone replacement therapy or topical treatment are eligible. 10. Has had an allogeneic tissue/solid organ transplant except for corneal transplantation. 11. Active infection requiring systemic treatment. 12. Active infection with HIV and CD4+ T-cell count \<350/μL. Patients not on established antiretroviral therapy for at least 4 weeks and having a detectable HIV viral load. Testing is not required for eligibility. 13. Active infection with hepatitis B (surface antigen); or infection with hepatitis C, defined by a detectable viral load. Testing is required for eligibility only if patient has a known or suspected history of infection. 14. Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 6 months of enrollment, unstable angina, congestive heart failure (New York Heart Association class ≥ II), or serious uncontrolled cardiac arrhythmia requiring medication. 15. History or current evidence of any condition, therapy, any active infections, or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate, in the opinion of the treating Investigator. 16. Known psychiatric or substance abuse disorder that would interfere with cooperation with the requirements of the study. 17. Legally incapacitated or has limited legal capacity. 18. Pregnant or breastfeeding.