Pemetrexed Disodium and Sorafenib Tosylate in Treating Patients With Advanced Solid Tumors

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