This is a Phase I open-label clinical trial to assess the safety, feasibility, and preliminary efficacy of intrapleural administration of MOv19-BBz CAR T cells in patients with FRa+ cancers. This study will be initiated in patients with metastatic or recurrent non-small cell lung cancer (NSCLC) only. Subjects will receive a single dose of MOv19-BBz CAR T cells via intrapleural infusion following lymphodepleting chemotherapy. Subjects without an existing intra-pleural catheter will have a temporary pleural catheter placed for the study. Subjects may initiate treatment with commercial checkpoint inhibitors per routine care beginning at least 28 days after receiving MOv19-BBz CAR T cells.