Study of Antibody Drug Conjugate in Patients With Advanced Breast Cancer Expressing HER2

Inclusion Criteria: * Able and willing to give informed consent * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Measurable disease via RECIST * Resolution of all toxic side effects from prior oncology treatments * Adequate organ function as measured by various blood parameters * Not pregnant or lactating, willing to prevent pregnancy while on study and for 6 months after the last dose of XMT-1522 * Histologically or cytologically confirmed adenocarcinoma of the breast with unresectable locally advanced disease, or metastatic disease and HER2 IHC 1+ or 2+ OR * Histologically or cytologically confirmed adenocarcinoma of the breast with unresectable locally advanced disease, or metastatic disease and HER2 IHC 3+ or positive for HER2 gene amplification * Progressed following all standard of care therapies for advanced breast cancer. OR * Histologically or cytologically confirmed locally advanced or metastatic gastric cancer and HER2 IHC 3+ or positive for HER2 gene amplification OR * Histologically or cytologically confirmed Stage IIIb or IV non-small cell lung cancer HER2 IHC 2+ or 3+ by local laboratory assessment. Exclusion Criteria: * Major surgery, radiation therapy, or systemic anti-cancer therapy within 28 days of starting study treatment. * Some types of brain metastases * Peripheral neuropathy of Grade 2 within 3 weeks prior to the first study therapy * History of exposure to cumulative doxorubicin dose ≥ 360 mg/meter squared. If another anthracycline or more than one anthracycline has been used, then the cumulative dose must not exceed the equivalent of 360 mg/meter squared of doxorubicin * History of clinically significant cardiac dysfunction * Current known active infection with HIV, hepatitis B virus, or hepatitis C virus * Current severe, uncontrolled systemic disease * Severe dyspnea at rest, due to complications of advanced malignancy, or requiring supplementary oxygen therapy. * History of other malignancy within the last 5 years, except for appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, or other malignancy with a similar expected curative outcome Patients who participate in the dose escalation segment of the study cannot participate in the expansion segment of the study.