Additional Study Information: XMT-1536 (upifitamab rilsodotin) is a targeted therapy, which means that it is directed specifically at a tumor. It is a type of antibody-drug conjugate; this means it has 2 parts that are joined together into one drug. The first part is an antibody that binds to NaPi2b (sodium-dependent phosphate transporter), a protein on the surface of the cells of your tumor. The second part is a cancer medicine that is attached to the antibody. When the antibody binds to NaPi2b, it carries the cancer medicine directly into the tumor cells to kill them. XMT-1536 is the study drug and a placebo is an inactive drug or treatment used in a clinical trial. Subjects will be randomized and blinded into the two groups after you finish your treatment with carboplatin and taxol. A computer will decide which group you are put in. You have an equal chance of getting XMT-1536 or placebo. You, your study doctor, and the study staff won't know whether you are getting XMT-1536 or placebo. In case of a health emergency, they can find out. The purpose of the study is to compare progression-free survival (the length of time that participants live without their disease getting worse) for participants with ovarian cancer with high NaPi2b level on their tumor cells treated with XMT-1536 versus placebo following standard chemotherapy, compare response to treatment and overall survival, compare safety and tolerability of treatment with XMT-1536 versus treatment with placebo, compare the time to the start of next cancer treatment after study treatment with XMT-1536 or placebo and the time to worsening of participants cancers following next cancer treatment, understand quality of life through participant questionnaires, and evaluate if blood levels of XMT-1536 and proteins your body may produce that can bind to XMT-1536 are related to response to treatment or side effects of treatment.