This phase I trial studies the side effects and best dose of giving pemetrexed disodium and sorafenib tosylate together in treating patients with advanced solid tumors. Pemetrexed disodium and sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Sorafenib tosylate may also stop the growth of solid tumors by blocking blood flow to the tumor. Giving pemetrexed disodium together with sorafenib tosylate may kill more tumor cells.

PRIMARY OBJECTIVES:

I. To determine doses for the combination of pemetrexed (pemetrexed disodium) with sorafenib (sorafenib tosylate) appropriate for Phase II study.

SECONDARY OBJECTIVES:

I. To evaluate the safety, tolerance, and toxicity of the combination of pemetrexed and sorafenib.

II. To observe antitumor effects of the combination.

OUTLINE: This is a dose-escalation study of pemetrexed disodium and sorafenib tosylate.

Patients receive pemetrexed disodium intravenously (IV) on day 1 every 2 weeks and sorafenib tosylate orally (PO) twice daily (BID) on days 1-5. Courses repeat every 4 weeks in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 30 days.

Inclusion Criteria:

• Advanced solid tumor malignancy for which there is no potentially curative treatment; there is no limit to the number of prior lines of therapy
• Performance status Eastern Cooperative Oncology Group (ECOG) equal or less than 1
• Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =< 3 x upper institutional limit (ULN)
• Total bilirubin =< 1.5 ULN
• Creatinine clearance (CrCl) >= 45 mL/min as measured by the standard Cockcroft-Gault equation
• International normalized ratio (INR) =< 1.5 (if not due to anticoagulants)
• White blood cell count (WBC) >= 3,000 cells/mm3
• Absolute neutrophil count (ANC) >= 1,500 cells/mm3
• Platelets >= 100,000 cells/mm3
• Hemoglobin (Hgb) >= 8.5 g/dL
• Prior toxicities are allowed as long as they are stable and would not interfere with study drug toxicity assessment
• Measurable or evaluable disease by Response Evaluation Criteria In Solid Tumors (RECIST) (v 1.1)
• Ability to understand and the willingness to sign a written informed consent document; a signed informed consent must be obtained prior to any study specific procedures
• Women of childbearing potential must have a negative pregnancy test performed within 7 days prior to the start of treatment; women of childbearing potential and men must agree to use a medically accepted form of birth control for the duration of study participation; men must agree to use a medically accepted form of birth control for 2 months following completion of study treatment

Exclusion Criteria:

• Any investigational agent within 4 weeks of first dose of study treatment
• Unwillingness or inability to take folic acid, vitamin B12, or dexamethasone
• Known or presumed intolerance of pemetrexed or sorafenib; unable to swallow medication; suspected malabsorption
• Active illicit substance or alcohol abuse
• Contraindication to antiangiogenic agents, including:
• Pulmonary hemorrhage/bleeding event >= Grade 2 within 4 weeks or less prior to the first dose of study drug
• Any other hemorrhage/bleeding event >= Grade 3 within 4 weeks or less prior to the first dose of study drug
• Serious non-healing wound, ulcer, or bone fracture
• Thrombolic or embolic events such as a myocardial infarction, cerebrovascular accident including transient ischemic attacks within the past 6 months
• Major cardiac dysfunction, such as uncontrolled angina, congestive heart failure with New York Heart Association (NYHA) class III or higher, ventricular arrhythmias requiring anti-arrhythmic therapy
• Systolic blood pressure > 160 mmHg or diastolic pressure > 100 mmHg despite optimal medical management
• Inability to interrupt aspirin or other nonsteroidal anti-inflammatory agents for a 5 day period
• Serious uncontrolled infection > Common Terminology Criteria for Adverse Events (CTCAE) (v 4) grade 2
• Peripheral motor or sensory neuropathy>CTCAE (v4) grade 2
• Uncontrolled metastatic brain disease
• Serum B12 or folate levels below the institution's lower limit of normal. Patients may begin B12/folic acid supplementation and can be reconsidered for study once levels meet the eligibility requirements
• Administration of non-steroidal anti-inflammatory drugs (NSAIDs) within 5 days prior to pemetrexed dosing (note: if a candidate routinely takes NSAIDs prior to enrollment, consider transition to alternate non-NSAID for duration of study treatment, if possible).
• Other condition(s) that in the opinion of the investigator might compromise the objectives of the study