Inclusion Criteria

          -  Histologically or cytologically confirmed invasive metastatic breast cancer (MBC) or
             locally advanced breast cancer (LABC) that is incurable, unresectable, and previously
             treated with multimodality therapy

          -  Measurable disease that is evaluable per Response Evaluation Criteria in Solid Tumors
             (RECIST) v1.1

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1

          -  Willing to provide tumor biopsy sample at the time of screening

          -  Local histological or cytological confirmation of estrogen receptor (ER) and/or
             progesterone receptor status as defined by using immunohistochemistry (IHC) per
             American Society of Clinical Oncology/College of American Pathologists criteria

          -  Percentage of ER and/or progesterone receptor positivity, if available

          -  Willing to provide blood samples at the time of screening, on-study, and at
             progression for exploratory research on biomarkers

          -  HER2-positive BC as defined by an IHC score of 3+ or gene amplified by in situ
             hybridization (ISH) as defined by a ratio of >/= 2.0 for the number of HER2 gene
             copies to the number of chromosome 17 copies

          -  Adequate hematologic and end-organ function

          -  Screening left ventricular ejection fraction (LVEF) >/= 50% on echocardiogram (ECHO)
             or multiple-gated acquisition (MUGA) scan

          -  Negative HIV test, hepatitis B surface antigen (HBsAg), total hepatitis B core
             antibody (HBcAb) test at screening, or positive total HBcAb test followed by a
             negative hepatitis B virus (HBV) DNA test at screening

          -  Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody
             test followed by a negative HCV RNA test at screening

          -  For women of childbearing potential: agreement to remain abstinent (refrain from
             heterosexual intercourse) or use contraceptive methods that result in a failure rate
             of < 1% per year during the treatment period and for at least 30 days after the last
             dose of venetoclax or 7 months after the last dose of trastuzumab emtansine

          -  For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use
             contraceptive methods, and agreement to refrain from donating sperm during the
             treatment period and for at least 30 days after the last dose of venetoclax or 7
             months after the last dose of trastuzumab emtansine

        Inclusion Criteria for Expansion Phase Only

        In addition to the general inclusion criteria, participants in the expansion phase must
        also meet the following criteria for study entry:

          -  Trastuzumab emtansine experienced cohort: Disease progression during or after
             trastuzumab emtasine in the advanced/metastatic setting or disease recurrence in the
             neoadjuvant/adjuvant setting; At least 50% of participants in the expansion cohort
             must have a tumor that is Bcl-2 high (defined as >50% of tumor cells stained with an
             intensity of immunohistochemistry (IHC) 2+ or 3+)

          -  Trastuzumab deruxtacan (DS-8201a) experienced cohort: Disease progression during or
             after trastuzumab deruxtecan in the advanced/metastatic setting; Prior trastuzumab
             emtansine in any setting is allowed; At least 50% of participants in the expansion
             cohort must have a tumor that is Bcl-2 high

        Exclusion criteria

          -  Receipt of any anticancer drug/biologic or investigational treatment 21 days prior to
             Cycle 1, Day 1 except hormone therapy, which can be given up to 7 days prior to Cycle
             1, Day 1

          -  Radiation therapy within 2 weeks prior to Cycle 1, Day 1

          -  History of exposure to the following cumulative doses of anthracyclines as specified:
             Doxorubicin >500 mg/m2; Liposomal doxorubicin >500 mg/m2; Epirubucin >720 mg/m2;
             Mitoxantrone >120 mg/m2; Idarubicin >90 mg/m2. If another anthracycline or more than
             one anthracycline has been used, then the cumulative dose must not exceed the
             equivalent of 500 mg/m2 doxorubicin.

          -  History of other malignancy within the previous 5 years

          -  Cardiopulmonary dysfunction

          -  Current severe, uncontrolled systemic disease

          -  Major surgical procedure or significant traumatic injury within 28 days prior to
             randomization or anticipation of the need for major surgery during the course of study
             treatment

          -  Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection
             (excluding fungal infections of nail beds) at study enrollment, or any major episode
             of infection requiring treatment with IV antibiotics or hospitalization (relating to
             the completion of the course of antibiotics) within 4 weeks prior to Cycle 1, Day 1

          -  Clinically significant history of liver disease, including cirrhosis, current alcohol
             abuse, autoimmune hepatic disorders, sclerosis cholangitis, or active infection with
             HBV or HCV)

          -  Uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia

          -  Known HIV infection or human T-cell leukemia virus 1 infection

          -  Spinal cord compression not definitively treated with surgery and/or radiation, or
             previously diagnosed and treated spinal cord compression without evidence that disease
             has been clinically stable for > 2 weeks prior to randomization

          -  Known central nervous system (CNS) disease

          -  Leptomeningeal disease

          -  Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent
             drainage procedures

          -  Uncontrolled hypercalcemia or symptomatic hypercalcemia requiring continued use of
             bisphosphonate therapy

          -  Current Grade >/= 3 peripheral neuropathy

          -  History of severe allergic, anaphylactic, or other hypersensitivity reactions to
             chimeric or humanized antibodies, excipients of any drugs formulated in polysorbate 80
             or 20 or fusion proteins

          -  Prior allogeneic stem cell or solid organ transplantation

          -  Pregnant or breastfeeding, or intending to become pregnant during the study or within
             30 days after the last dose of venetoclax or 7 months after the last dose of
             trastuzumab emtansine after the final dose of study treatment, whichever is later

          -  Consumption of grapefruit, grapefruit products, Seville oranges, or starfruit within 3
             days before anticipated first dose of study drug until the last dose of study drug

          -  Administration of a live, attenuated vaccine within 4 weeks prior to initiation of
             study treatment or anticipation of need for such a vaccine during the study

          -  Illicit drug or alcohol abuse within 12 months prior to screening, in the
             investigator's judgment

          -  Malabsorption syndrome or other condition that would interfere with enteral absorption

          -  History of active inflammatory bowel disease (e.g., Crohn's disease or ulcerative
             colitis) requiring specific medication in the 12 months prior to randomization, or
             active and uncontrolled bowel inflammation (e.g., diverticulitis) at time of
             randomization

          -  Inability or unwillingness to swallow a large number of tablets

          -  Known hypersensitivity to venetoclax or trastuzumab emtansine or to any of their
             excipients

          -  Any serious medical condition or abnormality in clinical laboratory tests that, in the
             investigator's judgment, precludes the patient's safe participation in and completion
             of the study

          -  Other medical or psychiatric conditions that, in the opinion of the investigator, may
             interfere with the patient's participation in the study

          -  Blood transfusions if performed within 2 weeks prior to screening

        Exclusion Criteria for Randomized Phase II Stage

        In addition to the general exclusion criteria, participants in the randomized Phase II
        stage who meet the following criteria will be excluded:

          -  Prior treatment with trastuzumab emtansine in any setting (neoadjuvant/adjuvant or
             advanced/metastatic setting)

          -  Prior treatment with venetoclax in any setting

          -  Prior treatment with anti-HER2 antibody drug conjugates (e.g. trastuzumab deruxtecan
             [DS-8201a]), margetuximab, pyrotinib, or tucatinib)