Inclusion Criteria:

          -  Men and women who are ≥18 years old.

          -  Pathologically confirmed advanced solid tumor cancers

          -  For Cohort 1, documented activating HER2 mutation in lung cancer by CLIA laboratory,
             specifically exon 20 insYVMA (Y772_A775dup), insGSP (G778_P780dup), insTGT
             (G776delinsVC), single base pair substitutions L755A, L755S, V777L, V659E, S310F, or
             another HER2 mutation approved by the Principal Investigator

          -  For Cohorts 2, 3, 4, documented HER2 amplification identified through next generation
             sequencing by MSK-IMPACT or at another Clinical Laboratory Improvement Amendments
             (CLIA) laboratory, or documented HER2 amplification by in-situ hybridization (ISH)
             with HER2/CEP17 ratio ≥2.0 at a CLIA laboratory. Patients with HER2 amplification
             identified by another method or criteria must be approved by the Principal
             Investigator and may enroll in the "Other" Cohort 4.

          -  Measurable or evaluable indicator lesion(s) as defined by RECIST v1.1. Patients
             without RECIST measurable disease will be eligible for enrollment to "Other" cohort
             provided their disease can be evaluated using another accepted response criteria (e.g.
             Gynecologic Cancer InterGroup (GCIG) CA125 Response Criteria, PET Response Criteria in
             Solid Tumors (PERCIST).

          -  Karnofsky Performance Status 70% or above.

          -  Left ventricular ejection fraction (LVEF) ≥50% measured by echocardiogram (ECHO) or
             multiple gated acquisition scan (MUGA).

          -  Negative β-human chorionic gonadotropin (hCG) pregnancy test within 2 weeks before
             enrollment for premenopausal women of reproductive capacity and for women less than 12
             months after menopause. Pregnancy screening will be conducted for women up to the age
             of 50 years per institutional standard.

          -  Women of child bearing potential must agree to use of a highly effective method of
             contraception from the time of informed consent until 6 months after the last dose of
             ado-trastuzumab emtansine. Men must agree to use a barrier method of contraception
             while on treatment and for 6 months after the last dose of ado-trastuzumab emtansine.

          -  Absolute neutrophil count ≥ 1,000/µL within 30 days prior to C1D1

          -  Platelet count ≥ 100,000/µL within 30 days prior to C1D1

          -  Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN), in case of
             Gilbert's syndrome, ≤ 2x ULN within 30 days prior to C1D1

          -  Aspartate aminotransferase and/or alanine aminotransferase ≤ 3 x ULN (≤ 5 x ULN if
             liver metastases are present) within 30 days prior to C1D1

          -  Provide written, informed consent to participate in the study and follow the study
             procedures

        Exclusion Criteria:

          -  Prior therapy resulting in cumulative epirubicin dose ≥ 900mg/m2 or cumulative
             doxorubicin dose ≥ 500mg/m2 or equivalent dose of another anthracycline.

          -  Prior therapy with ado-trastuzumab emtansine (patients who had prior trastuzumab or
             other HER2 targeted agents are eligible).

          -  Symptomatic congestive heart failure (New York Heart Association Classification
             II-IV).

          -  Myocardial infarction or unstable angina within 6 months of enrollment.

          -  Unstable ventricular arrhythmia requiring treatment.

          -  Grade 3 or worse peripheral neuropathy as defined by CTCAE v4.1.

          -  Women who are pregnant or breast-feeding.

          -  Known hypersensitivity to any component of ado-trastuzumab emtansine.