Additional Study Information: The purpose of the study is to compare how well Rina-S works against ovarian cancer, primary peritoneal cancer, or fallopian tube cancer compared to chemotherapy drugs that are already approved and used for your type of cancer. You have an equal (50:50) chance of getting Rina-S or an approved chemotherapy agent as treatment in this study. Rina-S is not approved by the United States Food and Drug Administration (FDA) because it is still undergoing clinical trials. Rina-S is a type of drug called an antibody-drug conjugate, or "ADC". An antibody-drug conjugate (ADC) is a cancer treatment that combines a monoclonal antibody (mAb) with a drug to deliver chemotherapy directly to cancer cells. Antibody-drug conjugates (ADCs) are Antibody-drug conjugates (ADCs) are like "guided missiles" for cancer treatment. They combine the precision of antibodies with the power of chemotherapy drugs. The antibody finds and binds to specific cancer cells, and then the drug is released inside the cancer cell, killing it without harming healthy cells. It contains 2 parts linked together: 1. Antibody: a protein that sticks to a target (called FR) on cancer cells in your body, 2. Toxin: a chemotherapy drug, called exatecan, that kills the cancer cells. The antibody (protein) and the toxin are chemically linked so that the toxin is not released from the ADC until it is inside the target cells. Rina-S may also affect some non-cancer cells in your body. There are four standard chemotherapy drugs that can be used in this study: 1) paclitaxel, 2) topotecan, 3) pegylated liposomal doxorubicin (PLD), and 4) gemcitabine. If you get standard chemotherapy as your study treatment, your study doctor will choose one of these drugs for you.