This phase III trial compares the effect of immunotherapy (IO) with stereotactic body radiation therapy (SBRT) to IO alone in treating patients with liver cancer (hepatocellular cancer) that may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced). The usual approach is treatment with IO-based drug combinations, such as atezolizumab and bevacizumab, durvalumab and tremelimumab, or ipilimumab and nivolumab. IO with monoclonal antibodies, such as durvalumab, tremelimumab, atezolizumab, nivolumab and ipilimumab, may help the body's immune system attack the tumor, and may interfere with the ability of tumor cells to grow and spread. Bevacizumab is in a class of medications called antiangiogenic agents. It works by stopping the formation of blood vessels that bring oxygen and nutrients to tumor. This may slow the growth and spread of tumor cells. Radiation therapy uses high energy x-rays, particles, or radioactive seeds to kill cancer cells and shrink tumors. SBRT is a type of external radiation therapy that uses special equipment to position a patient and precisely deliver radiation to tumors in the body (except the brain). The total dose of radiation is divided into smaller doses given over several days. This type of radiation therapy helps spare normal tissue. Giving IO with SBRT may be more effective than IO alone in helping patients with advanced hepatocellular cancer live longer.

PRIMARY OBJECTIVE:

I. To determine if liver SBRT in combination with IO-based systemic therapy improves survival compared to IO-based systemic therapy alone, in patients with hepatocellular cancer with macrovascular invasion.

SECONDARY OBJECTIVES:

I. To evaluate and compare progression-free survival between treatment arms. II. To evaluate and compare objective response rate between treatment arms. III. To evaluate and compare vascular recanalization between treatment arms. IV. To evaluate and compare biochemical decline in alpha-fetoprotein (AFP) between treatment arms.

V. To evaluate and compare toxicity within and between treatment arms. VI. To evaluate and compare liver decompensation per Child Pugh score between treatment arms.

VII. To evaluate and compare liver decompensation per modified albumin-bilirubin (ALBI) (mALBI) score between treatment arms.

HEALTH-RELATED QUALITY OF LIFE (HRQOL) OBJECTIVES:

I. Primary: To compare Functional Assessment of Cancer Therapy-Hepatobiliary (FACT-Hep) total score at 6 months between the treatment arms.

II. Secondary: To evaluate and compare quality-adjusted survival using European Quality of Life Five Dimension (EQ-5D) between treatment arms. (Will be done if the overall survival primary endpoint is met and/or if EQ-5D significantly differs between treatment arms.) III. Exploratory: To evaluate FACT-Hep total scores over time between the treatment arms.

EXPLORATORY OBJECTIVES:

I. Biospecimen collection for future correlative analyses.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM 1: Patients receive 1 of 3 IO-based systemic treatments per physician's decision.

TREATMENT A: Patients receive atezolizumab and bevacizumab intravenously (IV) every 3 weeks in the absence of disease progression or unacceptable toxicity.

TREATMENT B: Patients receive tremelimumab IV once and durvalumab IV every 4 weeks in the absence of disease progression or unacceptable toxicity.

TREATMENT C: Patients receive nivolumab and ipilimumab IV every 3 weeks for up to 4 doses followed by nivolumab IV every 4 weeks in the absence of disease progression or unacceptable toxicity.

ARM 2: Patients receive 1 of 3 IO-based systemic treatments per physician's decision.

TREATMENT A: Patients undergo liver SBRT once daily (QD), once every other day (QOD), or twice weekly for 5 fractions over up to 3 weeks. Patients also receive atezolizumab and bevacizumab IV every 3 weeks in the absence of disease progression or unacceptable toxicity.

TREATMENT B: Patients undergo liver SBRT QD, QOD, or twice weekly for 5 fractions over up to 3 weeks. Patients also receive tremelimumab IV once and durvalumab IV every 4 weeks in the absence of disease progression or unacceptable toxicity.

TREATMENT C: Patients undergo liver SBRT QD, QOD, or twice weekly for 5 fractions over up to 3 weeks. Patients also receive nivolumab and ipilimumab IV every 3 weeks for up to 4 doses followed by nivolumab IV every 4 weeks in the absence of disease progression or unacceptable toxicity.

Additionally, patients undergo blood sample collection, chest computed tomography (CT) and CT and/or magnetic resonance imaging (MRI) throughout the study and may also undergo positron emission tomography (PET)/CT prior to registration.

After completion of study treatment, patients are followed every 3 months for 2 years, every 6 months for 3 years then yearly.

Inclusion Criteria:

• PRIOR TO STEP 1 REGISTRATION:

• Diagnosis of hepatocellular carcinoma (HCC) by at least 1 criterion listed below:

  • Pathologically (histologically or cytologically) proven diagnosis of HCC (strongly recommended)
  • Radiographically proven (American Association for the Study of Liver Diseases [AASLD] criteria) diagnosis of HCC by multiphasic MRI and/or CT scan is allowed.
  • For patients with a prior or concurrent malignancy, pathologic confirmation of hepatocellular cancer is required.

• HCC macrovascular invasion, defined as enhancing vascular thrombosis demonstrating arterial enhancement and venous or delayed venous washout on multiphasic MRI and/or CT is required.

• Presence of extrahepatic metastatic disease on CT chest and CT or MRI pelvis, or PET/CT chest/abdomen/pelvis is permitted.

• 5 or fewer discrete intrahepatic parenchymal foci of HCC.

• Total maximal sum of hepatocellular carcinoma tumors, as a single conglomerate, multiple lesions, or infiltrative HCC < 20 cm in total summed diameter.

• No direct primary tumor extension into the stomach, duodenum, small bowel, or large bowel.

• No known fibrolamellar HCC, sarcomatoid HCC, or biphenotypic HCC.

• Child-Pugh class A or B7 liver function.

• Age ≥ 18.

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2.

• Not pregnant and not nursing

  • Negative urine or serum pregnancy test (in persons of childbearing potential) within 30 days prior to registration. Childbearing potential is defined as any person who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal.

• Absolute neutrophil count (ANC) ≥ 1,500 cells/mm^3.

• Platelets ≥ 60,000 cells/mm^3.

• Hemoglobin ≥ 8g/dl (Note: The use of transfusion or other intervention to achieve hemoglobin [Hgb] ≥ 8g/dl is acceptable).

• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 6 x institutional upper limit of normal (ULN).

• Total bilirubin < 4 x institutional ULN.

• Creatinine clearance (CrCL) ≥ 30 mL/min/1.73 m^2 by the Cockcroft-Gault formula.

• For treatment of HCC:

  • Prior surgical resection, transarterial chemoembolization (TACE), and ablation are permitted.
  • No prior systemic therapy or transarterial radioembolization (TARE) for HCC.
  • No history of liver transplantation.

• For prior treatment for any malignancy:

  • Prior systemic therapy for a different cancer is allowable, except for prior immunotherapy.
  • No prior radiotherapy to the region of the study cancer that would result in significant overlap of radiation therapy fields that would lead to excessive cumulative toxicity at the discretion of the investigator.

• No medical contraindication to the standard of care immunotherapy.

• For patients to be treated with atezolizumab/bevacizumab:

  • No history of a gastrointestinal (GI) bleed or other clinically significant bleeding event within 6 months prior to study registration.

• Systemic immunostimulatory agents (including, but not limited to, interferons and interleukin-2 [IL-2]) are prohibited within 4 weeks or five drug elimination half-lives (whichever is longer) prior to registration and during the study period.

• No history of allergic reaction to the systemic therapy agent(s), compounds of similar chemical or biologic composition to the systemic therapy agent(s) (or any of its excipients).

• PRIOR TO STEP 2 RANDOMIZATION:

• Obtain confirmation of payment coverage (insurance or other) for both possible treatment arms.

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