Inclusion Criteria:

          -  Signed informed consent

          -  Patient able and willing to comply with protocol

          -  Cytologically or histologically confirmed carcinoma of the breast.

          -  Incurable locally advanced or metastatic disease who have previously received up to
             two previous chemotherapy regimens in this setting. Patient must have progressed or
             relapsed on or after taxane and trastuzumab-based therapy.

          -  HER2-positive disease

          -  At least one measurable lesion according to RECIST version 1.1; or patients with non
             measurable lesions could be included with these exceptions:

             o patients with only blastic bone lesions / with only pleural, peritoneal or cardiac
             effusion, or meningeal carcinomatosis

          -  ≥ 18 years of age

          -  ECOG 0 or 1

          -  Life expectancy ≥ 3 months

          -  Adequate bone marrow function:

               -  Hemoglobin ≥ 10 g/dl.

               -  Absolute neutrophil count ≥ 1.5 x 109/L.

               -  Platelets ≥ 100 x 109/L without transfusions within 21 days

               -  International normalized ratio (INR) < 1.5 × the upper limit of normal (ULN).

          -  Adequate hepatic and renal function

          -  Adequate cardiovascular function with LVEF ≥ 55%

          -  Recovery from all reported toxicities of previous anti-cancer therapies to baseline or
             grade ≤ 1 (CTCAE version 4.0), except for alopecia

          -  For women of childbearing potential and not postmenopausal, and who have not undergone
             surgical sterilization with a hysterectomy and/or bilateral oophorectomy, and men with
             partners of childbearing potential, use of forms of contraception

        Exclusion Criteria:

          -  Previous treatment with T-DM1 or anthracyclines

          -  More than two chemotherapeutic regimens for locally advanced incurable disease or
             metastatic disease

          -  Prior anti-cancer treatment with chemotherapy, immunotherapy or radiotherapy within 3
             weeks (6 weeks for nitrosoureas or mitomycin-C), hormonal therapy or lapatinib within
             7 days, prior trastuzumab within 21 days (7 days if weekly trastuzumab) or any other
             targeted therapy within the last 21 days prior to starting study treatment

          -  Previous radiotherapy for the treatment of unresectable, locally advanced/recurrent or
             mBC is not allowed if:

               -  The last fraction of radiotherapy has been administered within 21 days prior to
                  first study drug administration (except for brain irradiation; at least 28 days
                  will be required)

               -  More than 25% of marrow-bearing bone has been irradiated

          -  History of intolerance (including Grade 3 or 4 infusion reaction) or hypersensitivity
             to the active substance or to any of the excipients of T-DM1 or non-pegylated
             liposomal doxorubicin

          -  Patients with CNS involvement. However, patients with metastatic CNS tumors may
             participate in this trial if the patient is > 4 weeks from radiotherapy completion, is
             clinically stable with respect to CNS tumor at the time of study entry and is not
             receiving steroid therapy for brain metastases

          -  Severe/uncontrolled intercurrent illness including, but not limited to, ongoing or
             active infection, or psychiatric illness/social situations that would limit compliance
             with study requirements.

          -  Cardiopulmonary dysfunction

          -  Current peripheral neuropathy of Grade ≥ 3 per the NCI CTCAE, v4.0

          -  History of a decrease in LVEF to < 40% or symptomatic CHF with previous trastuzumab
             treatment

          -  Prior malignancy, other than carcinoma in situ of the cervix, or non-melanoma skin
             cancer, unless the prior malignancy was cured ≥ 5 years before first dose of study
             drug with no subsequent evidence of recurrence

          -  Current known active infection with HIV, hepatitis B, and/or hepatitis C virus

          -  Women who are pregnant or breast-feeding