Mirvetuximab Soravtansine and Rucaparib Camsylate in Treating Participants With Recurrent Endometrial, Ovarian, Fallopian Tube or Primary Peritoneal Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed: * Recurrent endometrial cancer (all histologies, including carcinosarcoma) * Recurrent ovarian, primary peritoneal (female only), or fallopian tube cancer * all histologies except low grade serous or clear cell carcinoma unless the patient has a known somatic or germline breast cancer (BRCA) mutation disease that is metastatic and for which standard curative measures do not exist or are no longer effective * For the dose escalation portion of the trial, patients with available therapies known to confer clinical benefit (platinum sensitive ovarian cancer) must be excluded * For the dose expansion cohort, patients with recurrent endometrial cancer, recurrent BRCA mutated ovarian cancer (except first-recurrence platinum sensitive ovarian cancer), and platinum resistant ovarian cancer are eligible * Patients must have confirmation of folate receptor-a (FR-alpha) positivity by immunohistochemistry (IHC) (? 25% of tumor staining at ? 2 + intensity) on archival tissue or recent biopsy. * Patients must be willing and able to undergo tissue biopsy for research * If tumor tissue obtained from the biopsy is deemed inadequate, and the patient is unwilling or unable to have another biopsy, the patient may be considered for enrollment if archival tumor tissue is provided and deemed of adequate quality; this must occur prior to any treatment with rucaparib or mirvetuximab soravtansine * If bi…