Inclusion Criteria

- Unresectable breast cancer involving chest wall, regional nodes, or distant site

- Breast cancer determined to be ER-negative and PgR-negative defined for this study as
< 10% tumor staining by 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
Oncologists/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).

- Disease progression during or after treatment for recurrent or metastatic disease

- A minimum of 1 previous chemotherapy regimen for treatment of recurrent or metastatic
disease

- 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 (untransfused)

- 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

- International normalized ratio (INR) 1.5

- 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 pemetrexed

- Toxicities from previous cancer therapies resolved to grade 1 unless specified
otherwise in the inclusion or exclusion criteria (Exception: Neuropathy related to
previous chemotherapy must be resolved to grade 2.)

- 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) 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

- Known or presumed intolerance of pemetrexed or sorafenib

- Known or suspected malabsorption condition or obstruction

- Symptomatic or untreated brain metastases (Note: Patients with known brain metastases
who are asymptomatic and have had post-treatment imaging that indicates stable
disease in the brain are eligible. Also, note that imaging of the brain is required
within 8 weeks prior to study registration).

- 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 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

- QTcF interval > 450 ms ( grade 1) on electrocardiogram (ECG)

- If baseline QTcF on screening ECG is grade 1:

- Check potassium and magnesium serum levels

- Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to confirm
exclusion of patient due to QTcF

- 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 QTcF
(Note: If heart rate is 60-100 bpm, manual read of 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 (Note: Patients with small effusions remaining after
pleurodesis are eligible. Determination of eligibility based on pleural size will be
determined by the principal investigator).

- 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 administration of a STRONG CYP3A4 inducer (Note: The reference list
of cytochrome p450 (CYP) isozymes and classification of strong, moderate, and weak
interactions is available through the FDA website).

- Pregnancy or breastfeeding

- Diagnosis or treatment for another malignancy within 3 years of enrollment, with the
following exceptions: complete resection of basal cell carcinoma or squamous cell
carcinoma of the skin, any in situ malignancy, and low-risk prostate cancer after
curative therapy

- 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

Minimum Eligible Age: 18 Years

Maximum Eligible Age: N/A

Eligible Gender: Both