2nd Line Treatment With Pemetrexed and Sorafenib for Recurrent or Metastatic Triple Negative Breast Cancer

Inclusion Criteria * Unresectable adenocarcinoma of the breast involving chest wall, regional nodes, or distant site * Breast cancer determined to be estrogen receptor (ER)-negative and progesterone receptor (PgR)-negative defined for this study as \< 10% tumor staining by immunohistochemistry (IHC) (Note: Eligibility should be based on the ER and PgR status reported at the time of the most recent biopsy or resection). * Breast cancer determined to be HER2-negative per current American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) HER2 Guidelines (Note: Eligibility should be based on the HER2 status reported at the time of the most recent biopsy or resection). * At least one prior regimen for treatment of recurrent or metastatic disease (Note: Prior regimen for recurrent or metastatic disease is not required if the patient had disease progression or recurrence during or within the first 6 months following completion of adjuvant or neoadjuvant chemotherapy.) * Measurable disease per RECIST v1.1 * Age ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Ability to swallow oral medications * Adequate bone marrow function as defined below: * Absolute neutrophil count (ANC) ≥ 1,200/mm3 * Platelet count ≥ 100,000/mm3 * Hemoglobin ≥ 9.0 g/dL, which must be stable in the opinion of the investigator without a history of transfusion dependence. * Adequate renal function as defined below: * Calculated creatinine clearance ≥ 45 mL/min * Adequate hepatic function as defined below: * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) for the laboratory * Aspartate aminotransferase (AST) ≤ 3 x ULN for the laboratory, except in the presence of known hepatic metastasis, wherein the AST may be ≤ 5 x ULN * Alanine aminotransferase (ALT) ≤ 3 x ULN for the laboratory, except in the presence of known hepatic metastasis, wherein the ALT may be ≤ 5 x ULN * Serum B12 and folate levels ≥ lower limit of normal (LLN) for the laboratory (Note: Patients may begin B12 and folic acid supplementation and be reconsidered for participation in the study when levels are ≥ LLN for the laboratory). * Ability to take folic acid, vitamin B12, and dexamethasone according to the protocol instructions * Ability to interrupt chronic non-steroidal anti-inflammatory drugs (NSAIDs) beginning 2 days before (5 days before for long-acting NSAIDs) and continuing for 2 days following administration of each pemetrexed dose * Toxicities from previous cancer therapies resolved to ≤ grade 1 unless specified otherwise in the inclusion or exclusion criteria * Women who are not postmenopausal or have not undergone hysterectomy must have a documented negative serum pregnancy test within 7 days prior to initiating study treatment. Note: Postmenopausal is defined as one or more of the following: * Age ≥ 60 years * Age \< 60 years and amenorrheic for at least 1 year with follicle-stimulating hormone (FSH) and plasma estradiol levels in the postmenopausal range * Bilateral oophorectomy * A woman of child-bearing potential (WCBP) and a male patient with partner who is a WCBP must agree to use a medically accepted method for preventing pregnancy for the duration of study treatment and for 2 months following completion of study treatment. * Ability to understand and willingness to sign the consent form written in English Exclusion Criteria * Any investigational agent within 4 weeks prior to initiating study treatment * Anticancer therapy within 2 weeks prior to initiating study treatment * Plans for concurrent anticancer therapy except as permitted in Section 6.7.11 * Known or presumed intolerance of pemetrexed or sorafenib * Known or suspected malabsorption condition or obstruction * Brain metastases meeting either of the following exclusion criteria: * Untreated brain metastases * After completion of brain-directed therapy, the patient has not been able to tolerate discontinuation of steroids or a decrease in steroid dose * Leptomeningeal metastasis * Any documented history of clinically identifiable thrombotic, embolic, venous, or arterial events such as cerebrovascular accident, transient ischemic attack, deep vein thrombosis, or pulmonary embolism within 6 months prior to initiating study treatment (Note: Patients with an asymptomatic catheter-related thrombus or a tumor-associated thrombus of locally-involved vessels or with incidental asymptomatic filling defects identified on imaging are not excluded.) * Contraindication to antiangiogenic agents, including: * Serious non-healing wound, non-healing ulcer, or bone fracture * Major surgical procedure or significant traumatic injury within 4 weeks prior to initiating study treatment * Pulmonary hemorrhage/bleeding event ≥ grade 2 (CTCAE v4.0) within 12 weeks prior to initiating study treatment * Any other hemorrhage/bleeding event ≥ grade 3 (CTCAE v4.0) within 12 weeks prior to initiating study treatment * Systolic blood pressure (BP) \> 160 mmHg or diastolic BP \> 100 mmHg despite optimal medical management * QT interval, corrected (QTc) \> 480 ms (≥ grade 2) on a 12-lead electrocardiogram (ECG) * If baseline QTc on screening ECG is ≥ grade 2: * Check potassium and magnesium serum levels * Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to confirm exclusion of patient due to QTc * For patients with heart rate \< 60 bpm or \> 100 bpm, manual read of the QT interval by a cardiologist is required, with Fridericia correction applied to determine QT interval with correction using Fridericia's formula (QTcF) which must be used to determine eligibility (Note: If heart rate is 60-100 bpm, manual read of the QT interval and correction to QTcF is not required). * Active or clinically significant cardiac disease including any of the following: * Unstable angina (eg, anginal symptoms at rest) or onset of angina within 3 months prior to initiating study treatment * Myocardial infarction within 6 months prior to initiating study treatment * Ventricular arrhythmias requiring anti-arrhythmic therapy other than beta blockers * New York Heart Association (NYHA) class III or IV congestive heart failure * Serious (ie, ≥ grade 3) uncontrolled infection * Uncontrolled effusion * Known human immunodeficiency virus (HIV) seropositivity (Note: HIV testing is not required) * Chronic or active hepatitis B or C infection requiring treatment with antiviral therapy * Seizure disorder requiring enzyme-inducing anti-epileptic drugs (EIAEDs) (Note: If the seizure disorder can be managed with agents that are not EIAEDs (eg, levetiracetam or valproate), the patient should not be excluded). * Planned ongoing treatment with other drugs thought to potentially have adverse interactions with either of the study drugs; if such drugs have been used, patients must have discontinued these agents at least 2 weeks (or as noted below) prior to initiating study treatment. Examples include: * STRONG CYP3A4 inducers \*Note: Examples of clinical inducers of cytochrome p450 (CYP) isozymes and classification of strong, moderate, and weak interactions are available through the FDA website (Table 3-3 of website:): http://www.fda.gov/Drugs/DevelopmentApprovalProcess/DevelopmentResources/DrugInteractionsLabeling/ucm093664.htm * Immunosuppressants (eg, tacrolimus, leflunomide, tofacitinib, roflumilast, pimecrolimus) * NSAIDs (Note: NSAIDs must be discontinued within 5 days prior to initiating study treatment) * Pregnancy or breastfeeding * Previous malignancy with the following exceptions: adequately treated basal cell carcinoma or squamous cell carcinoma of the skin; any in situ malignancy; adequately treated Stage 1 and Stage 2 cancer from which the patient is currently in remission; any other cancer from which the patient has been disease-free for 3 years * Medical, psychological, or social condition that, in the opinion of the investigator, may increase the patient's risk or limit the patient's adherence with study requirements