This is an open-label, Phase 1a dose escalation study of OMP-31M32 administered as a single agent to evaluate the safety, tolerability pharmacokinetics, and pharmacodynamics in patients with locally advanced or metastatic solid tumors. This study consists of a screening period, a treatment period and a post-treatment follow-up period in which patients will be followed for survival for up to 2 years. Subjects will be enrolled in two stages: a dose escalation stage and an expansion stage.