Testing the Addition of an Anti-cancer Drug, Sapanisertib, to the Usual Chemotherapy Treatment (Cabozantinib) in Metastatic Liver Cell Cancer With a Change in Genes for the Protein β-Catenin, The SAPHIRE Trial

Inclusion Criteria: * Patients must have histologically or cytologically confirmed HCC, not amenable to curative treatment approach * For Phase 2, patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥ 20 mm (≥ 2 cm) by chest x-ray or as ≥ 10 mm (≥ 1 cm) with CT scan, MRI, or calipers by clinical exam * For phase 2, patients must have a β-catenin mutation, based on next generation eequencing (NGS) testing through Clinical Laboratory Improvement Amendments (CLIA)-certified commercially available standard of care assay * Patients must have received at least one prior line of systemic therapy in the metastatic setting, including a prior immune checkpoint inhibitor therapy unless not eligible. For the phase 2 portion, patients must have received at least one and no more than two prior lines of systemic therapy in the metastatic setting, including a prior immune checkpoint inhibitor therapy unless not eligible * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of sapanisertib in combination with cabozantinib in patients \<18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 50%) * Child Pugh score of A * Absolute neutrophil count ≥ 1,000/mcL * Platelets ≥ 30,000/mcL * Total bilirubin ≤ 1.5 × in…