Maintenance Zanzalintinib and Durvalumab in Participants With Advanced Hepatocellular Cancer

Inclusion Criteria: * Participants must have radiographically or histologically or cytologically confirmed hepatocellular cancer. Participants must have advanced cancer (metastatic or unresectable) requiring systemic therapy. * Participants must be treated with tremelimumab plus durvalumab and have stable disease or response to therapy. Participants must have received 2 to 5 doses of durvalumab prior to starting treatment on the clinical trial. * Age \>18 years. Because no dosing or adverse event data are currently available on the use of durvalumab in combination with zanzalintinib in participants ≤18 years of age, children are excluded from this study. * ECOG Performance status 0-2. * Participants must have normal organ and marrow function as defined below based upon meeting all the following laboratory criteria within 14 days before first dose of study treatment: * Absolute neutrophil count ≥ 1,500/mcL 1,500/mcL (without granulocyte colony-stimulating factor support within 2 weeks of screening laboratory sample collection) * Hemoglobin ≥ 9 g/dL (≥ 90 g/L) without transfusion within 2 weeks prior to screening laboratory sample collection. * Platelet count ≥ 75,000/mcL * Total bilirubin \< 2.0 mg/dL or \<2x upper limit of normal (ULN) whichever is higher * AST (SGOT) ≤ 5 X institutional upper limit of normal * ALT (SGPT) ≤ 5 X institutional upper limit of normal * Creatinine clearance ≥ 40 mL/min (≥ 0.67 mL/sec) using the Cockcroft Gault equation * International Normalized Ratio (INR) ≤ 1.7 and/or activated partial thromboplastin time (aPTT) ≤ 1.2 x ULN. * Serum albumin at least 2.5g/dL for Child-Pugh A * Urine protein-to-creatinine ratio (UPCR) ≤ 1 mg/mg (≤ 113.2 mg/mmol) creatinine * Child Pugh Score A 5-6 * Participants must have the ability to understand and the willingness to sign a written informed consent document. * At least one index lesion that is measurable based on RECIST 1.1. * Recovery to baseline or ≤ Grade 1 severity (CTCAE v5) from AEs, including immune-related adverse events (irAEs), related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy (eg, physiological replacement of corticosteroid). Low-grade or controlled toxicities such as alopecia, ≤ Grade 2 fatigue, ≤ Grade 2 hypomagnesemia, ≤ Grade 2 neuropathy are permitted) * Sexually active fertile participants and their partners must agree to use highly effective method of contraception during the course of the study and for the following durations after the last dose of zanzalintinib or duvalumab whichever was administered later. An additional contraceptive method, such as a barrier method (eg, condom), is required. In addition, men must agree not to donate sperm and women must agree not to donate eggs (ova, oocyte) for the purpose of reproduction during these same periods. * through 186 days after the last dose of zanzalintinib or durvalumab for women of childbearing potential (WOCBP) or through 96 days after the last dose of zanzalintinib or durvalumab for men * Female participants of childbearing potential must not be pregnant at screening. Female participants are considered to be of childbearing potential unless one of the following criteria is met: permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes. In addition, females \< 55 years-of-age must have a serum follicle stimulating hormone \[FSH\] level \> 40 mIU/mL to confirm menopause). Note: Documentation may include review of medical records, medical examination, or medical history interview by study site staff. Exclusion Criteria: * Inability to swallow tablets or ingest a suspension either orally or by a nasogastric (NG) or gastrostomy (PEG) tube. * Participants receiving any other investigational agents concurrently for cancer treatment. * Participants with untreated brain metastases/CNS disease will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of solid organ or allogeneic stem cell transplant. * Participants with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. This includes unstable or deteriorating cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, class 2 or higher, unstable angina pectoris, new-onset angina, serious cardiac arrhythmias (eg, ventricular flutter, ventricular fibrillation, Torsades de pointes). * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic despite optimal antihypertensive treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction, or other clinically significant arterial thrombotic and/or ischemic event within 6 months before first dose of study treatment. * Pulmonary embolism (PE) or deep vein thrombosis (DVT) or prior clinically significant venous events within 3 months before first dose of study treatment. * Note: Participants with a diagnosis of DVT within 6 months are allowed if asymptomatic and stable at screening and are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen. Note: Participants who don't require prior anticoagulation therapy may be eligible but must be discussed and approved by the Principal Investigator. * Prior history of myocarditis. * Gastrointestinal (GI) disorders associated with a high risk of perforation or fistula formation: * Tumors invading the GI-tract from external viscera * Active peptic ulcer disease, inflammatory bowel disease, diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, or acute pancreatitis * Acute obstruction of the bowel, gastric outlet, or pancreatic or biliary duct within 6 months before first dose unless cause of obstruction is definitively managed and participant is asymptomatic * Abdominal fistula, gastrointestinal perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose. Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose of study treatment. * Known gastric or esophageal varices * Ascites, pleural effusion, or pericardial fluid requiring drainage in last 4 weeks * Active infection requiring systemic treatment. Note: Prophylactic antimicrobial treatments (antibiotics, antimycotic, antiviral) are allowed. * Known infection with acute or chronic hepatitis B or C, known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness except for participants meeting all of the following criteria: (1) on stable anti-retroviral therapy; (2) CD4+ T cell count ≥ 200/µL; and (3) an undetectable viral load. Note: HIV testing will be performed at screening if and as required by local regulation. Note: To be eligible, participants taking CYP inhibitors (eg, zidovudine, ritonavir, cobicistat, didanosine) or CYP3 inducers (efavirenz) must change to a different regimen not including these drugs 7 days prior to initiation of study treatment. Anti-retroviral therapies (ART) must have been received for at least 4 weeks prior to the first dose. Note: CD4+ T cell counts, and viral load are monitored per standard of care by the local health care provider. Following illnesses/conditions are also excluded * Serious non-healing wound/ulcer/bone fracture. Note: non-healing wounds or ulcers are permitted if due to tumor-associated skin lesions. * Malabsorption syndrome. * Pharmacologically uncompensated, symptomatic hypothyroidism. * Requirement for hemodialysis or peritoneal dialysis * Prior treatment with tyrosine kinase inhibitors for HCC * Another malignancy that requires active therapy and in the opinion of the Investigator would interfere with monitoring of radiologic assessments of response to Investigational Product, within 2 years before first dose of study treatment, except for superficial skin cancers, or localized, low-grade tumors deemed cured and not treated with systemic therapy. Incidentally diagnosed prostate cancer is allowed if assessed as stage ≤ T2N0M0 and Gleason score ≤ 6. * Active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids (prednisone \>10 mg daily orally) or immunosuppressive agents. Participants with durvalumab related adverse event can be included in the trial as long as participants are not requiring prednisone (or equivalent) \> 20 mg daily dosing. * Pregnant or breastfeeding women are excluded from this study because durvalumab and zanzalintinib has the potential for teratogenic effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother, breastfeeding should be discontinued if the mother is treated on clinical trial. These potential risks may also apply to other agents used in this study. * Radiation therapy for bone metastasis within 2 weeks, any other radiation therapy within 4 weeks before first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before first dose of study treatment. Participants with clinically relevant ongoing complications from prior radiation therapy are not eligible. * Concomitant anticoagulation with oral anticoagulants (eg, warfarin, direct thrombin inhibitors ) and platelet inhibitors (eg, clopidogrel). Note: Participants must have discontinued oral anticoagulants within 3 days or 5 half-lives prior to first dose of study treatment, whichever is longer. Allowed anticoagulants are the following: * Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH). * Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, or apixaban in participants without known brain metastases who are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen. * Any complementary medications (eg, herbal supplements or traditional Chinese medicines) to treat the disease under study within 2 weeks before first dose of study treatment. * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (eg, pulmonary hemorrhage) within 12 weeks before first dose of study treatment. * Lesions invading major blood vessel including, but not limited to, inferior vena cava, pulmonary artery, or aorta. Note: Participants with intravascular tumor extension (eg, tumor thrombus in renal vein or inferior V. cava) may be eligible following Principal Investigator approval. Participants with involvement of portal vein or hepatic vessels are allowed to participate. * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 480 ms within 14 days per electrocardiogram (ECG) before first dose of study treatment. * Note: Triplicate ECG evaluations will be performed and the average of these 3 consecutive results for QTcF will be used to determine eligibility. * History of psychiatric illness likely to interfere with ability to comply with protocol requirements or give informed consent. * Previously identified allergy or hypersensitivity to components of the study treatment formulations. * Any active, known, or suspected autoimmune disease. Note: Participants with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Known positive test for tuberculosis infection if supported by clinical or radiographic evidence of disease. * History of idiopathic pulmonary fibrosis, organizing pneumonia (eg, bronchiolitis obliterans), drug induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computerized tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted. * Free thyroxine (FT4) outside the laboratory normal reference range. Asymptomatic participants with FT4 abnormalities can be eligible after Principal Investigator approval. * Administration of a live, attenuated vaccine within 30 days before first dose of study treatment. * Documented hepatic encephalopathy (HE) within 6 months before first dose of study treatment. * Clinically meaningful ascites (ie, ascites requiring repeated paracentesis) within 6 months before first dose of study treatment. * Participants who have received any local anticancer therapy including surgery, PEI, RFA, MWA, trans arterial chemoembolization (TACE), or trans arterial radioembolization (TARE) within 28 days prior to first dose of study treatment. Major surgery (eg, GI surgery, removal or biopsy of brain metastasis) within 8 weeks prior to first dose of study treatment. Prior laparoscopic surgeries (ie nephrectomy) within 4 weeks prior to first dose of study treatment. Minor surgery (eg, simple excision, tooth extraction) within 5 days before first dose of study treatment. Complete wound healing from major or minor surgery must have occurred at least prior to first dose of study treatment.