The primary purpose of this study is to help answer the following research questions:

• whether the chemotherapy combination therapy Pemetrexed-Carboplatin or Gemcitabine-Vinorelbine can help participants with advanced breast cancer to make the tumor smaller or disappear and for how long
• to learn more about the side effects in each chemotherapy combination treatment arm
• to assess how participants with advanced breast cancer report health changes while receiving any of the chemotherapy combination arm

Inclusion Criteria:

• Females with histologic or cytologic diagnosis of advanced breast cancer. Lesions should not be amenable to surgery or radiation of curative intent.
• Performance status of 0 to 2 on the Eastern Cooperative Oncology Group (ECOG) performance status scale.
• One prior chemotherapy containing anthracyclines as (neo)adjuvant or palliative 1st-line treatment.
• One prior chemotherapy containing taxanes as (neo) adjuvant or palliative 1st-line treatment.
• Prior radiation therapy is allowed to less than 25% of the bone marrow. Participants must have recovered from the toxic effects of the treatment prior to study enrollment (except for alopecia). Prior radiotherapy must be completed 30 days before study entry. Lesions that have been radiated cannot be included as sites of measurable disease unless clear tumor progression has been documented in these lesions since the end of radiation therapy.
• At least one uni-dimensionally measurable lesion meeting Response Evaluation Criteria in Solid Tumors (RECIST) criteria. Positron emission tomography [PET] scans and ultrasounds may not be used.
• Antitumoral hormonal treatment must be discontinued prior to enrollment.
• Estimated life expectancy of at least 3 months.
• Participant compliance and geographic proximity that allow adequate follow-up.
• Adequate organ function
• Female participants of childbearing potential must test negative for pregnancy within 7 days of enrollment based on a urine and/or serum pregnancy test and agree to use a reliable method of birth control during and for 6 months following the last dose of study drug.
• Participants must sign an informed consent document.
• Female participants must be at least 18 years of age.

Exclusion Criteria:

• Have received treatment within the last 30 days with a drug that has not received regulatory approval for any indication at the time of study entry.
• Have previously completed or withdrawn from this study or any other study investigating Pemetrexed, Gemcitabine, Carboplatin or Vinorelbine
• Have received more than one line of chemotherapy in Metastatic Breast Cancer. Participants having received more than one combination of anthracycline plus taxane.
• Are pregnant or breast-feeding.
• Have serious concomitant systemic disorders (e.g., active infection) that, in the opinion of the investigator, would compromise the safety of the participant or compromise the participant's ability to complete the study.
• Have a prior malignancy other than breast cancer, carcinoma in situ of the cervix, or nonmelanoma skin cancer, unless that prior malignancy was diagnosed and definitively treated at least 5 years previously with no subsequent evidence of recurrence.
• Are unable to interrupt aspirin or other nonsteroidal anti-inflammatory agents for a 5-day period (8-day period for long-acting agents such as piroxicam), unless the Creatinine Clearance is greater than or equal to 80 ml/min.
• Have central nervous system (CNS) metastases.
• Have clinically relevant (by physical exam) third-space fluid collections (for example, ascites or pleural effusions) that cannot be controlled by drainage or other procedures prior to study entry.
• Are unable or unwilling to take folic acid, vitamin B12 supplementation, or dexamethasone.
• Concurrent administration of any other antitumor therapy.