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

The dose escalation segment of the study utilizes a 3+3 design. Initially, 3 patients will be dosed at each dose level. The first 3-week cycle of treatment constitutes the dose limiting toxicity (DLT) evaluation period. If none of the 3 patients experience a DLT during the evaluation period and the Safety Review Committee agrees this was a reasonably well tolerated dose, 3 patients will be enrolled at the next dose level. However, in the event of 1 DLT, 3 additional patients will be enrolled at the same dose level. Any dose level with 2 or more DLTs will be considered to have exceeded the maximum tolerated dose and subsequent patients will be enrolled at lower dose levels. After the first cycle, patients may continue to receive XMT-1522 until disease progression as long as the drug is well-tolerated and patients continue to derive clinical benefit in the opinion of the Investigator. After completion of the dose escalation, the expansion segment will enroll the patients with the following kinds of cancer: * Cohort 1: Advanced breast cancer, HER2 IHC 1+, or HER2 IHC 2+ without HER2 gene amplification * Cohort 2: Advanced breast cancer, HER2-positive, who have received prior ado-trastuzumab emtansine * Cohort 3: Advanced gastric cancer, HER2-positive, who have received prior trastuzumab * Cohort 4: Advanced non-small cell lung cancer, HER2 IHC 2+ or 3+, any HER2 gene amplification or mutation status