The main purpose of this study is to see whether the combination of trametinib and sorafenib can help people with hepatocellular cancer. Researchers also want to find out if the combination of trametinib and sorafenib is safe and tolerable.

Each cycle will last for 4 weeks. Sorafenib and trametinib will be administered orally on continuous basis. During the first cycle sorafenib will be started on day 1 and trametinib on day 8 to improve tolerance. Participants will get restaging scans every 2 cycles. Participants will continue to receive treatment if they have a stable disease or a better response by Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1.

Inclusion Criteria:

• Must have radiographic or histological diagnosis of hepatocellular cancer (HCC), with advanced stage disease that is not amenable to curative surgical resection. Potential participants without histologic diagnosis must meet the radiographic criteria for HCC.
• Child Pugh score must be 5 or 6 (Child Pugh Class A)
• Must have measurable disease by RECIST criteria 1.1
• Eastern Cooperative Oncology Group (ECOG) performance status ≤1
• Must have normal organ and marrow function
• Female participants of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male participants must use an effective barrier method of contraception if sexually active with a female of child-bearing potential. For both male and female participants, effective methods of contraception must be used throughout the study and for four months following the last dose.
• Able to swallow and retain orally administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels
• Participants in the dose expansion part must have tumor that is amenable for biopsy.
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Have received radiation therapy, major surgery, other locoregional therapy, within 4 weeks prior to the first dose of study drug
• All prior treatment-related toxicities must be ≤ Grade 1.
• Have received sorafenib or other systemic therapies for treatment of HCC in the past
• Any serious and/or unstable pre-existing medical disorder (aside from malignancy exception), psychiatric disorder, or other conditions that could interfere with participant's safety, obtaining informed consent or compliance to the study procedures
• History or evidence of cardiovascular risk
• Known history of human immunodeficiency virus (HIV) positivity
• History of retinal vein occlusion (RVO)
• Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression
• History of interstitial lung disease or pneumonitis
• Are pregnant or lactating
• Any underlying condition that would significantly interfere with the absorption of an oral medication
• History of another active malignancy in last 3 years. Exception: Potential participants who have been disease-free for 3 years, or have a history of completely resected nonmelanoma skin cancer and/or potential participants with indolent second malignancies are eligible.
• Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose; patients with controlled infection or on prophylactic antibiotics are permitted in the study
• Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to study drug, or excipients or to dimethyl sulfoxide
• Concurrent therapy with approved or investigational anticancer therapy
• Concomitant use of strong Cytochrome P450 3A4 (CYP3A4) inducers