• To determine the objective response rate with trabectedin in patients with the following metastatic breast cancer subtypes:Group A: triple negative profile (ER-, PR-, HER-2-) Group B: human epidermal growth factor receptor-2 overexpressing tumors (HER-+) [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Tumor response rate [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  

• Duration of response, Progression-free survival, Exploratory evaluation of changes in tumor volume and changes in tumoral radiological density, Safety profile, Exploratory, hypothesis-generating pharmacogenomic analyses [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Duration of response [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Duration of Progression-free survival [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Changes in tumor volume [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Changes in tumoral radiological density [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: No ]
  
• Adverse events [ Time Frame: Up to approximately 24 months ] [ Designated as safety issue: Yes ]
  

This is an open-label, clinical trial evaluating the effectiveness and safety of trabectedin in three subpopulations of breast cancer patients: Group A: triple negative profile (ER-, PR-, HER-2-), Group B: human epidermal growth factor receptor-2 overexpressing tumors (HER-2+) and Group C: familial BRCA1 or BRCA2 mutation carrier. Each subtype is defined according to the estrogen, progesterone, and the Human Epidermal Growth Factor Receptor- 2 (HER-2) status in the primary tumor (present or overexpressing = positive or absent or do not overexpressing = negative) or the history of having BRCA1 or BRCA2 mutation genes. Trabectedin will be administered intravenously (iv) every three weeks. Patients will be assessed weekly physical exam and / or laboratory testing. Radiological examination will occur every 6 weeks to evaluate the patient's disease. Treatment will continue as long as the patient tolerating trabectedin and their disease is stable or improving. Duration of response, progression free-survival, exploratory evaluation of changes in tumor volume and changes in tumoral radiological density, safety profile and exploratory, hypothesis-generating pharmacoecogenomic analyses will be assessed.Patients are evaluable for safety if they received at least part of one infusion of trabectedin. Safety will be assessed by adverse events, laboratory measurements, and clinical examinations Trabectedin will be administered intravenously (iv) at a dose of 1.3 mg/m2 over 3-hours (hrs) on Day 1 of every 21-day treatment cycle. In addition, patients will be administered dexamethasone on Day 1 of each treatment cycle as follows: 4mg orally (PO) 24h and 12h before the trabectedin iv infusion, 20 mg, iv 30 minutes before the trabectedin infusion, and 4 mg PO 24h, 36h, 48h, 60h, 72h, after the start of trabectedin infusion.