This is a multi-center study of XMT-1536 in patients with tumors likely to express NaPi2b, focusing on patients with platinum-resistant ovarian cancer and non-squamous non-small cell lung cancer. XMT-1536 will be administered as an intravenous infusion once every three weeks. The study consists of two segments: dose escalation (DES) and expansion (EXP). The DES segment will study small groups of patients who receive increased doses. A Safety Review Committee will be established to review the data from each dose level before moving to the next higher dose. Dose escalation will stop when a patient or patients experience 2 or more dose-limiting events. At this point, the maximum tolerated dose or recommended Phase 2 dose will be established and the EXP segment will begin. This segment consists of 3 parallel cohorts of patients to confirm the MTD or RP2D and estimate the objective response rate in each selected patient population. All adverse events will be graded according to the National Cancer Institute (NCI) Common Terminology Criteria version (CTCAE v4.03). Throughout the study, pharmacokinetics will be measured using proprietary assays developed by Mersana. ADC activity will be measured via RECIST.