This Phase 1b trial is an open label, multi-center study of XMT-1522 administered as an intravenous infusion once every three weeks. The dose escalation part of the study will establish the maximum tolerated dose or recommended Phase 2 dose for in patients with advanced breast cancer and either a HER2 immunohistochemistry (IHC) score of at least 1+ using a validated IHC assay or with evidence of HER2 amplification. Patients with HER2 positive (by IHC or amplification) gastric cancer or nonsmall cell lung cancer may also be eligible for participation in dose escalation. Upon completion of dose escalation, the cohort expansion segment of the study will consist of four parallel cohorts of different patients groups to confirm the maximum tolerated dose or the recommended Phase 2 dose and estimate the objective response in each of the patient populations.