AGEN1884, an Anti-CTLA-4 Human Monoclonal Antibody in Participants With Advanced or Refractory Cancer and Who Have Progressed With PD-1/PD-L1 Inhibitor as Their Most Recent Therapy

Inclusion Criteria: 1. Written informed consent. 2. ≥18 years of age. 3. Histological or cytological diagnosis of solid cancer or lymphoma that is considered incurable and without therapies with established benefit. Biopsy is not necessary for participants with known prior diagnosis, and clinical or radiographic evidence of recurrence. For Phase 2 only: Participants who experienced documented disease progression during treatment with an approved or investigational PD-1/PD-L1 inhibitor as their most recent therapy (2-6 weeks prior to first dose of study drug). This cohort includes participants with histological diagnoses of hepatocellular carcinoma (HCC) (not including atypical histology such as cholangiocarcinoma mix or fibrolamellar hepatocellular carcinoma) who experienced documented disease progression during treatment with an approved or investigational PD-1/PD-L1 inhibitor as their most recent therapy (2-6 weeks prior to first dose of study drug). 4. Eastern Cooperative Oncology Group (ECOG) score of 0 or 1. 5. Participants in Phase 2 with HCC should have a Child-Pugh score of A or B7 with no encephalopathy or ascites. 6. Life expectancy ≥12 weeks. 7. Adequate cardiac function (New York Heart Association \[NYHA\] class ≤II). 8. Adequate organ function, defined as absolute neutrophil count (ANC) ≥1,500×10\^6/liter (L), absolute lymphocyte count ≥500/cubic millimeters (mm\^3), hemoglobin ≥8.0 grams/deciliter (g/dL), and platelet count ≥100,000×10\^6/mm\^3 without blood growth factors or without transfusions within 1 week of first dose. For participants in Phase 2 with HCC: Platelet count ≥60×10\^6/mm\^3 and ANC ≥1,000×10\^6/L are acceptable provided that the principal investigator assesses these abnormalities as due to liver disease. 9. Adequate liver function, defined as aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.5× institutional upper limit of normal (ULN), and bilirubin ≤1.5 milligrams/deciliter (mg/dL) × ULN. For participants in Phase 2 with HCC: AST and ALT ≤5 × ULN, bilirubin ≤2 mg/dL × ULN, and albumin ≥2.8 mg/dL. 10. Adequate renal function, defined as estimated creatinine clearance ≥50 milliliters/minute according to Cockcroft-Gault formula, or measured 24-hour creatinine clearance (or local institutional standard method). 11. Adequate coagulation defined by international normalized ratio (INR) or prothrombin time (PT) ≤1.5× ULN (unless the participant is receiving anticoagulant therapy); and activated partial thromboplastin time ≤1.5× ULN (unless the participant is receiving anticoagulant therapy). Participants in Phase 2 with HCC can have an INR ≤2.3× ULN. Note: Participants in Phase 2 with HCC and on anticoagulant treatment would have an assigned value of 1 point when scoring PT/INR so the overall Child-Pugh score is not adversely affected. 12. Female participants of childbearing potential and fertile male participants must agree to use adequate contraception or abstain from sexual activity from the time of consent through 90 days after the end of study drug. Adequate contraception includes condoms with contraceptive foam; oral, implantable, or injectable contraceptives; contraceptive patch; intrauterine device; diaphragm with spermicidal gel; or a sexual partner who is surgically sterilized or postmenopausal. Note: Abstinence is acceptable if this is the established and preferred contraception for the participant. 13. In the expansion phase, all participants must provide a sufficient and adequate formalin-fixed paraffin embedded (FFPE) tumor tissue sample preferably collected after progression on the last therapy and/or collected at screening, if clinically feasible. If a recent biopsy is not available, an archival FFPE sample should be provided from a site not previously irradiated. If no tumor tissue is available, a fresh biopsy will be required if clinically feasible. Exclusion Criteria 1. Other malignancies treated within the last 5 years, except in situ cervix carcinoma or non-melanoma skin cancer. 2. Other form(s) of antineoplastic therapy anticipated during the period of the study. 3. Previous severe hypersensitivity reaction to another fully human monoclonal antibody or severe reaction to immuno-oncology agents, such as colitis or pneumonitis requiring treatment with steroids. 4. History of interstitial lung disease. 5. Primary or secondary immunodeficiency, including immunosuppressive disease, autoimmune disease (including autoimmune endocrinopathies), or usage of immunosuppressive medications. Note: Participants with diabetes type 1, vitiligo, psoriasis, hypo-, or hyperthyroid disease not requiring immunosuppressive treatment are eligible. Participants with Type 2 diabetes mellitus are allowed. 6. Participants with a known history of human immunodeficiency virus 1 and 2, human T lymphotropic virus 1. Participants in Phase 2 with HCC: Participants with active hepatitis B infection who are receiving effective antiviral therapy are permitted. Participants with active hepatitis C infection are allowed (antiviral therapy not required). 7. Administration of anticancer medications or investigational drugs within the following intervals before the first administration of study drug: a. ≤14 days for chemotherapy, targeted small molecule therapy, or radiation therapy. Participants must also not have had radiation pneumonitis as a result of treatment and cannot participate in the study if they are on chronic corticosteroids for radiation pneumonitis. A 1-week washout is permitted for palliative radiation to non-central nervous system (CNS) disease, with medical monitor approval. Note: Bisphosphonates and denosumab are permitted medications. b. ≤14 days for prior immunotherapy. Participants in the dose escalation cohorts are excluded if they have received prior checkpoint inhibitors, costimulatory agonists, or immune modulating therapy except as described below. Once a dose level is determined to be safe by the safety review committee, participants will be allowed to enroll in dose-level expansion cohorts if they have received other non-CTLA-4 targeting immunotherapies. c. Participants enrolling in Phase 2 must have cancer that has progressed after prior treatment with an approved or investigational PD-1/PD-L1 inhibitor as their most recent therapy (2-6 weeks prior to first dose of study drug). The minimum requirement of 2 weeks (14 days) from prior anti-PD-1/PD-L1 therapy is to allow resolution of any lower-grade (≤2) adverse events observed with the therapy. If the investigator feels the participant has tolerated prior anti-PD-1/PD-L1 therapy well, then treatment with study agent may begin sooner. d. ≤7 days for prior corticosteroid treatment, with the following exceptions: * Use of an inhaled or topical corticosteroid is permitted. * Corticosteroid premedication for radiographic imaging for dye allergies is permitted. * Use of physiologic corticosteroid replacement therapy may be approved after consultation with the medical monitor. e. ≤21 days for prior monoclonal antibody used for anticancer therapy, with the exception of denosumab. This does not apply to participants being enrolled in Phase 2, who have received a PD-1/PD-L1 inhibitor as their most recent therapy (2-6 weeks prior to first dose of study drug; see above). f. ≤7 days for immunosuppressive-based treatment for any reason, with the exceptions noted above for prior corticosteroid treatment (exclusion criterion d). g. ≤21 days or 5 half-lives before first dose of study treatment for all other investigational study drugs or devices. For investigational agents with long half- lives (for example, \>5 days), enrollment before the fifth half-life requires medical monitor approval. h. For participants in Phase 2 with HCC \<6 weeks for prior locoregional therapy to the liver, for example, transcatheter chemoembolization, radiation, surgery, or radioembolization. 8. Has not recovered to grade ≤1 from toxic effects of prior therapy and/or complications from prior surgical intervention before starting therapy. Note: Participants with grade ≤2 neuropathy and alopecia are an exception and may enroll. 9. Uncontrolled infection or other serious medical illnesses. 10. History or presence of an abnormal electrocardiogram that, in the investigator's opinion, is clinically meaningful. 11. Any medical conditions that, in the opinion of the investigator, would preclude use of AGEN1884, including AGEN1884 hypersensitivity. 12. Women who are pregnant or breastfeeding. 13. Concurrent participation in other investigational drug trials. 14. Has a 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: Participants with history of brain metastases that have been treated may participate provided they show evidence of stable supra-tentorial lesions are obtained after treatment to the brain metastases. These imaging scans should both be 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. For individuals who received steroids as part of brain metastases treatment, steroids must be discontinued ≥7 days prior to first dose of study drug. 15. For participants in Phase 2 with HCC, the following exclusions also apply: 1. Recent encephalopathy episodes in the last 6 months. 2. Recent (within the last 6 months) gastro-esophageal varices bleeding. 3. Participant whose tumors have cardiac involvement, as determined by imaging.