A Study of Onapristone ER Alone Or In Combination With Anastrozole in Gynecologic Cancers That Respond to Progesterone

Inclusion Criteria: * Histologically confirmed diagnosis at MSK of either (1) granulosa cell ovarian cancer, (2) low grade serous ovarian/ primary peritoneal cancer, or (3) endometrioid endometrial cancer; with PR expression ≥1% by IHC on archival tissue taken within the prior 3 years or new biopsy if no archival tissue is available. IHC results do not have to be from MSK. * Measurable disease as defined by RECIST 1.1. Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension. Each lesion must be ≥10mm when measured by CT or MRI. Lymph nodes must be ≥15mm in short axis when measured by CT or MRI * Patients must have had one prior chemotherapy regimen for management of disease. Note: additional lines of chemotherapy, biologic or immunotherapy are allowed. * Recovery from effects of recent surgery, radiotherapy, or chemotherapy * At least 4 weeks out from their last dose of radiation therapy * At least 4 weeks post-op from any major surgical procedure * At least 3 weeks out from their last dose of chemotherapy and/or biologic/targeted therapy * Must be ≥ 18 years of age * Karnofsky Performance Status (KPS) of ≥ 70% * Women of child-bearing potential must have a negative pregnancy test within 14 days prior to commencement of study treatment * Women of child bearing potential must use an effective form of contraception during study and for at least 6 months after completion of study treatment * Laboratory Test Findings performed within 14 days prior to initiation of study drug showing: * Bone marrow function: * Absolute neutrophil count (ANC) ≥ 1,000/mcL * Platelets ≥ 75,000/mcL * Hemoglobin ≥ 8 g/dL * Renal function: °Creatinine ≤ 1.5 x ULN * Hepatic function: * Bilirubin ≤ 1.5 x ULN * AST and ALT ≤ 2.5 x ULN * Resolution of all acute toxic effects of prior therapy to NCI CTCAE (Version 5.0) Grade ≤ 1, with the exception of unresolved Grade 2 neuropathy and Grade 2 alopecia, which are allowed * Patient has recovered from any prior radiotherapy * Patients must be able to swallow tablets whole, without crushing Exclusion Criteria: * History of another invasive malignancy (other than non-melanoma skin cancer or curatively treated in situ carcinoma) with evidence of disease within the past 3 years * History of prior hormonal therapy (i.e., megesterol acetate, tamoxifen or aromatase inhibitors) for treatment of cancer within 28 days before starting study drug * Any psychological, familial, sociological or geographic condition that would potentially hamper compliance with the study protocol * Known brain metastasis which have not been treated or showed stability for ≥ 6 months * Patient has received an oral or IV corticosteroid within the prior 28 days and requires chronic corticosteroid therapy (excludes use of steroid premeds for CT allergy) * Uncontrolled hypertension (systolic BP ≥ 160 mmHg or diastolic BP ≥ 95mmHg) despite medical treatment. Patients with a history of hypertension are allowed provided blood pressure is controlled by anti-hypertensive treatment. * Clinically significant heart disease as evidenced by myocardial infarction or arterial thrombotic event within the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) Class II-IV heart disease or cardiac ejection fraction measurement of \< 50% at baseline * Refractory nausea and vomiting, requirement for parenteral hydration and/or nutrition, drainage gastrostomy tube, malabsorption, external biliary shunt, or significant small bowel resection that would preclude adequate study drug absorption * Anticipated or ongoing administration of anti-cancer therapies other than those administered in this study * Use of any prescription medication during the prior 28 days of first onapristone dosing that the investigator judges is likely to interfere with onapristone activity; specifically strong inhibitors or inducers, or sensitive substrates of cytochrome P450 CYP3A4. Investigators should consult the following table of clinically-relevant products http://medicine.iupui.edu/CLINPHARM/ddis/clinical-table.